# 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

Could someone answer this and explain how the answer was found?
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.)

isosceles, problem, solve, triangle 