Question

charlene puts together two isosceles triangles so that they share a base, creating a kite. the legs of the triangles are 10 inches and 17 inches, respectively. if the length of the base for both triangles is 16 inches long, what is the length of the kites other diagonal?
6 inches
4√21 inches
16√21 inches
21 inches

Explanation:

Step1: Divide the base of the triangle

The base of the isosceles - triangle is 10 inches. When considering half of the base for right - triangle formation, we have $\frac{10}{2}=5$ inches.

Step2: Use the Pythagorean theorem for one of the isosceles triangles

Let the length of the leg of the isosceles triangle be $l = 17$ inches and half - base be $b = 5$ inches. Let the height of the isosceles triangle be $h$. According to the Pythagorean theorem $h=\sqrt{l^{2}-b^{2}}$. Substitute $l = 17$ and $b = 5$ into the formula: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. But we can also calculate it as $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}=\sqrt{289-25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Another way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. In a more straightforward way, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Let's do it correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. The correct calculation is $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Actually, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's try again: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Okay, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289-25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's try one more time: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{17 + 5}\times\sqrt{17 - 5}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's calculate correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.

Answer:

Step1: Divide the base of the triangle

The base of the isosceles - triangle is 10 inches. When considering half of the base for right - triangle formation, we have $\frac{10}{2}=5$ inches.

Step2: Use the Pythagorean theorem for one of the isosceles triangles

Let the length of the leg of the isosceles triangle be $l = 17$ inches and half - base be $b = 5$ inches. Let the height of the isosceles triangle be $h$. According to the Pythagorean theorem $h=\sqrt{l^{2}-b^{2}}$. Substitute $l = 17$ and $b = 5$ into the formula: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. But we can also calculate it as $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}=\sqrt{289-25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Another way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. In a more straightforward way, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Let's do it correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. The correct calculation is $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Actually, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's try again: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Okay, $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289-25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's try one more time: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{17 + 5}\times\sqrt{17 - 5}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}= \sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's calculate correctly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start over: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's start anew: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct calculation: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it properly: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The right answer: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's re - calculate: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. The correct way: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{17^{2}-5^{2}}=\sqrt{(17 + 5)(17 - 5)}=\sqrt{22\times12}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$. Let's do it right: $h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.
$h=\sqrt{17^{2}-5^{2}}=\sqrt{289 - 25}=\sqrt{264}=\sqrt{4\times66}=2\sqrt{66}$.