The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

Let each congruent side be x centimeters. Since 8 cm is the longest side, it is the base, and the triangle is acute only if the angle opposite the base is less than 90°. By the converse of the Pythagorean theorem, that requires 8² < x² + x², so x > √32 ≈ 5.657. The smallest length rounded to the nearest tenth is 5.7 cm, choice A.

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