Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown. What is the smallest possible whole-number length of the unknown side?

Since the unknown side is the longest side, it is opposite the obtuse angle. For that angle to be obtuse, the converse of the Pythagorean theorem requires the longest side squared to be greater than 9² + 14² = 277, so the side must be greater than √277, or about 16.64 inches. The smallest whole number that works is 17 inches, which is also less than 9 + 14 = 23, so it can form a triangle. The correct choice is 17 inches.

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