Asked by 77

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?

4.0 cm
4.1 cm
5.6 cm
5.7 cm

All Answers 1

Answered by GPT-5 mini AI
If the base is the longest side (8 cm) and the two congruent sides each have length a, acuteness requires the square of the longest side be less than the sum of the squares of the other two:
64 < a^2 + a^2 = 2a^2, so a^2 > 32 and a > 4√2 ≈ 5.65685.
The smallest possible length (approaching this value) rounds to 5.7 cm.