# 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 48 . What are the lengths of sides A and B?

Oct 8, 2016

$a = b = 10$

#### Explanation:

Imagine the height of the triangle bisecting side c, thereby, forming two triangles. The area of one of these triangles is 24, its base is 6 and its height can be found using, $A = \left(\frac{1}{2}\right) b h$

$24 = \left(\frac{1}{2}\right) 6 h$

$h = 8$

The hypotenuse of this triangle is one of the two equal sides of the original triangle:

a² = b² = 6² + 8²

a² = b² = 100

$a = b = 10$