# 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 14  and the triangle has an area of 42 . What are the lengths of sides A and B?

Mar 17, 2016

$A = \sqrt{{6}^{2} + {7}^{2}} \implies A = 5 \sqrt{3} = B$

#### Explanation:

Given: Area of an isosceles triangle, A_Delta =42; C = 14
Required: Length of sides $A$ and $B$:
Solution: A_Delta = 1/2 C*h; C = 14; h= height
42=1/2 (14*h); h=6  Now the height forms a right angle triangle with hypotenuse of $A$ and sides of $h$ and $\frac{C}{2}$. So you can use the Pythagoras Theorem:
${A}^{2} = {h}^{2} + {\left(\frac{C}{2}\right)}^{2}$ you know $h$ and $\frac{C}{2} = 7$ solve of A
$A = \sqrt{{6}^{2} + {7}^{2}} \implies A = 5 \sqrt{3} = B$