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 5  and the triangle has an area of 35 . What are the lengths of sides A and B?

May 23, 2018

$\textcolor{b l u e}{A = B = \frac{809}{4} \approx 202.25}$

Explanation:

The area of a triangle is given by:

$\frac{1}{2} \text{base" xx "height}$

$\frac{1}{2} \left(5\right) h = 35 \implies h = 14$

$\boldsymbol{h}$ bisects $\boldsymbol{c}$, since this is an isosceles triangle.

By Pythagoras' theorem:

$A = B = \sqrt{{\left(\frac{5}{2}\right)}^{2} + {\left(14\right)}^{2}} = \frac{809}{4} \approx 202.25$

2 d.p.