Question

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 `36`. What are the lengths of sides A and B?

Answer 1

The length of sides `A and B` are `8.49(2dp) unit` each .

Explanation:

Side `C` is the base of the isoceles triangle, `A and B` are legs, and `x` be the altitude.
The area of triangle is `A_t=1/2*C*x or 36= 1/2*12*x or x=6`
`= (A^2-(C/2)^2)=x^2 or (A^2-(12/2)^2)= 36 or A^2-36= 36 or A^2=72 or A=sqrt72=+-8.485`.
Side can not be negative.

So the length of sides `A and B` are `8.49(2dp) unit` each.[Ans]