The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?

For the triangle to be acute, the angle opposite the longest side, 30 inches, must be less than 90°. Thus 30² < x² + x², so each congruent side must be greater than 30/√2 ≈ 21.213 inches. The perimeter is 30 + 2x, which can be just above 72.426 inches; rounded to the nearest tenth, the smallest possible perimeter is 72.4 inches. Choice C, 72.4 in., is correct.

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