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?

For an acute triangle, the square of the longest side must be less than the sum of the squares of the other two sides. Thus the unknown longest side x must satisfy x² < 5² + 8² = 89, so x < √89, or about 9.43 inches. The greatest whole-number length that works is 9 inches, choice B.

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