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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.
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.
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