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

Answer 1

If both 5 and 8 are legs, the hypotenuse is sqrt(5^2+8^2)=sqrt(89) ≈ 9.433.
If one is the hypotenuse (must be 8), the other leg is sqrt(8^2−5^2)=sqrt(39) ≈ 6.244.
Difference ≈ 9.433 − 6.244 = 3.189 ≈ 3.2 inches.

Answer: 3.2 inches.