Question

a right triangle has legs with lengths of 7 inches and 8.5 in. which expression, and which value, depicts the length of the hypotenuse? select two answers. $sqrt{7^{2}+8.5^{2}}$ 11.00 ft $sqrt{8.5^{2}-7^{2}}$ 11.01 ft $sqrt{7^{2}-8.5^{2}}$

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with leg lengths $a$ and $b$ and hypotenuse length $c$, the Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Here $a = 7$ and $b=8.5$. So the expression for the length of the hypotenuse is $\sqrt{7^{2}+8.5^{2}}$.

Step2: Calculate the value

First, calculate $7^{2}=49$ and $8.5^{2}=72.25$. Then $7^{2}+8.5^{2}=49 + 72.25=121.25$. And $\sqrt{121.25}\approx11.01$.

Answer:

$\sqrt{7^{2}+8.5^{2}}$, $11.01$ ft