# 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 7  and the triangle has an area of 112 . What are the lengths of sides A and B?

Mar 2, 2018

Side A and Side B both are $32.76 .$

#### Explanation:

Given Information
$a r e a = 112$
$S i \mathrm{de} C = 7$
Side A and Side B = ?

The area equation of a triangle is $A r e a = \frac{1}{2} \left(b a s e\right) \left(h e i g h t\right)$
We know the area, and the base (side C), so we solve for height.

$112 = \frac{1}{2} \left(7\right) \left(h e i g h t\right)$
$112 = 3.5 h e i g h t$
$h e i g h t = 32$

Now that we know the height, we can use the Pythagorean theorem to solve the side lengths.

${a}^{2} + {b}^{2} = {c}^{2}$ Recall theorem
${\left(7\right)}^{2} + {\left(32\right)}^{2} = {c}^{2}$ Solving for c
$49 + 1024 = {c}^{2}$
$c = \sqrt{1073}$
$c = 32.76$

Since side A and side B are the same length, then $32.76$ is the side length for both.