# Thread: Can anyone solve this Isosceles triangle problem

1. ## Can anyone solve this Isosceles triangle problem

A landscape designer uses 8-foot timbers to form a pattern of isosceles triangles along the wall of a building. If the area of each triangle is 24 square feet, and the two equal sides are 8 feet each, what is the base?

So this is the problem:
Side A = 8 feet
Side B = 8 feet
Side C = X
Area = 24 square feet

I'm currently studying modeling with Linear and Quadratic Functions if that helps.

2. Call the length of side C $\displaystyle 2x,$ (= your X), and the heigth of the triangle $\displaystyle y.$
Then, using the known area of the triangle, $\displaystyle xy=24,$ and using the Pythagoras theorem $\displaystyle x^2+y^2=64.$
Substitute for $\displaystyle y$ in the second equation and then solve this as a quadratic in $\displaystyle x^2.$
(I calculate $\displaystyle x=3.2915$, or $\displaystyle x=7.2915,$. But you should check these results.)
(And remember to double them for the length of C.)