# An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 32  and the triangle has an area of 108 . What are the lengths of sides A and B?

Aug 11, 2016

$= 17.37$

#### Explanation:

This is an isosceles triangle with $b a s e = 32$ and $h e i g h t = h$
Area of a triangle$= \frac{1}{2} \times 32 \times h = 108$
or
$= h = 108 \times \frac{2}{32} = 6.75$
In isosceles triangle $h$ divides $b a s e$ equally
In other words isosceles triangle is 2 equal right-angled triangle combined with each right-angled triangle having $b = \frac{32}{2} = 16 \mathmr{and} p = 6.75$
So side$A$=side $B = \sqrt{{16}^{2} + {6.75}^{2}} = 17.37$