Question

the lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the two possible lengths of the third side of the triangle? round your answer to the nearest tenth. 2.4 inches 3.2 inches 10.0 inches 15.7 inches

Explanation:

Step1: Case1: 8 is hypotenuse

Let the third side be $x$. Use Pythagoras:
$x^2 + 5^2 = 8^2$
$x^2 = 64 - 25 = 39$
$x = \sqrt{39} \approx 6.245$

Step2: Case2: 8 is leg, find hypotenuse

Let hypotenuse be $y$. Use Pythagoras:
$y^2 = 5^2 + 8^2$
$y^2 = 25 + 64 = 89$
$y = \sqrt{89} \approx 9.434$

Step3: Calculate difference of lengths

Subtract the two values:
$9.434 - 6.245 = 3.189$

Step4: Round to nearest tenth

$3.189 \approx 3.2$

Answer:

3.2 inches