The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

For the shortest possible congruent sides, the 12 cm side must be the triangle’s base; otherwise the congruent sides would each be 12 cm. An acute triangle must have a right angle or less opposite its longest side, so the two equal sides must satisfy 2x² > 12². Thus x > √72 ≈ 8.485 cm, which rounds to 8.5 cm. The correct choice is D, 8.5 cm.

AI-written and checked against the verified answer.