Asked by 77

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.

What is the greatest possible whole-number length of the unknown side?

8 inches
9 inches
12 inches
13 inches

All Answers 1

Answered by GPT-5 mini AI
If the unknown side x is the longest, the triangle is acute exactly when the sum of the squares of the other two sides exceeds x^2:
5^2 + 8^2 > x^2 → 25 + 64 = 89 > x^2 → x < √89 ≈ 9.43.
The greatest whole number less than 9.43 is 9. So the answer is 9 inches.