# 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 9  and the triangle has an area of 45 . What are the lengths of sides A and B?

May 7, 2018

color(blue)("Sides " a = b = 10.97 " units"

#### Explanation:

$c = 9 , A r e a = 45 , \text{ To find sides } a , b$

${A}_{t} = \left(\frac{1}{2}\right) c h , \text{ where " h " is the height}$

$h = \frac{2 \cdot 45}{9} = 10$

$a = b = \sqrt{{\left(\frac{c}{2}\right)}^{2} + {h}^{2}} = \sqrt{{4.5}^{2} + {10}^{2}} = 10.97$