# 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 8  and the triangle has an area of 88 . What are the lengths of sides A and B?

Jun 10, 2016

$\left\mid A \right\mid = \left\mid B \right\mid = 10 \sqrt{5}$

#### Explanation:

Viewing C as the base and denoting the height as $h$
the formula for the area of a triangle tell us that:
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} \cdot 8 \cdot h = 88$ (using the given values)

This implies that $h = 22$

Side A (or B) together with half the length of C and the height form a right-angled triangle (with A the hypotenuse).

Therefore
$\textcolor{w h i t e}{\text{XXX}} \left\mid A \right\mid = \sqrt{{4}^{2} + {22}^{2}} = \sqrt{500} = 10 \sqrt{5}$