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

Sep 20, 2016

$9.605$

#### Explanation:

ABC is an isosceles triangle. $\implies A = B$

Area $\left({A}_{r}\right) = \frac{1}{2} \times b \times H$

where b=base and h=height.

Given ${A}_{r} = 45 \mathmr{and} C = 12$

$\implies {A}_{r} = 45 = \frac{1}{2} \times 12 \times H$; (C=base=12)

$\implies H = \frac{45 \times 2}{12} = 7.5$

$\implies A = B = \sqrt{{7.5}^{2} + {6}^{2}} = \sqrt{92.25} = 9.605$