Question

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

Answer 1

Let "x" be the  longest side and "y" be each of remaining sides
If the triangle is аcute then:

y² + y² > x² 
2y² > 8²
2y² > 64
y² > 32
y > √32
y > 5.6 ← to the nearest tenth

This means the length of each of the remaining sides is more than 5.6 cm, so the smallest possible length of one of the two congruent sides is 5.7 cm.

Answer 2

the answer is D) 5.7cm