The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.What is the greatest possible whole-number value of the congruent side lengths?

Let each congruent side be x. Since the triangle’s longest side is 20 cm, the angle opposite that side is the obtuse angle, so the converse of the Pythagorean theorem gives 20² > x² + x². Thus x < √200, which is about 14.14. The triangle inequality also requires 2x > 20, and the greatest whole-number value satisfying these conditions is 14 cm, choice C.

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