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

Jun 20, 2018

Area=$\frac{1}{2} \times b a s e \times h e i g h t$

$42 = \frac{1}{2} \times 12 \times h e i g h t$

$h e i g h t = 7$

the height will bisect the base and create two right triangles where the hypotenuse of each will be the lengths A and B

Using Pythagoras ${a}^{2} + {b}^{2} = {c}^{2}$

${6}^{2} + {7}^{2} = {A}^{2}$

$36 + 49 = {A}^{2}$

$A = B = \sqrt{85}$