Question

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?

A) 6.0 cmB) 6.1 cmC) 8.4 cmD) 8.5 cm

Answer 1

8.4 cm

Explanation:

The longest side of an acute isosceles triangle is 12 centimeters.

Let x be the length of the smallest side

Isosceles triangle has one longest side and two smallest sides

so its acute triangle

`c^2<a^2 +b^2`

where c is the longest side

a and b are two shortest sides 'x'

`c^2<x^2 +x^2`

`12^2<x^2 +x^2`

`144<2x^2`

divide both sides by 2

`72<x^2`take square root on both sides

`8.4<x`

So 8.4 cm