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: Case 1 - Both legs

Third side (hypotenuse): $\sqrt{5^2 + 8^2} = \sqrt{89} \approx 9.43$ inches

Step2: Case 2 - 8 as hypotenuse

Third side (leg): $\sqrt{8^2 - 5^2} = \sqrt{39} \approx 6.24$ inches

Step3: Calculate difference

$9.43 - 6.24 \approx 3.19 \approx 3.2$ inches

Answer:

B. 3.2 inches