Question

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?

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 > 30²
2y² > 900
y² > 450
y > √450
y > 21.21 ← to the nearest hundredth

This means the length of each of the remaining sides is not less than 21.22 in  (to the nearest hundredth), so the smallest possible perimeter of the triangle =
30 + 21.22 + 21.22 = 72.44 in.