In the figure below, $AB=75,$ $AC=70,$ and $BY=60$. Compute $CX$.

Compute the area A of ∆ABC.

• Take AB to be the base and CX (which is an altitude of ∆ABC) to be the height. Then the area is

A = 1/2 • AB • CX = 1/2 • 75 • CX

• Now take AC to be the base and BY (also an altitude) to be the height. Then

A = 1/2 • AC • BY = 1/2 • 70 • 60 = 2100

The areas must be equal, so we have

2100 = 1/2 • 75 • CX   →   CX = 4200/75 = 56