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?

The longest side, 12 cm, is opposite the largest angle. For the triangle to be acute, that angle must be less than 90°, so the other two sides must satisfy 12² < x² + x². This gives x > 12/√2 ≈ 8.485 cm. The smallest possible length rounded to the nearest tenth is therefore 8.5 cm, choice A.

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