What is the height of this triangle? We have a triangle with sides 50, 70 and 80 and have drawn an altitude ('h') to side AB. We have segmented side AB into "x" and "80-x".
From the Pythagorean Theorem, we know that
h^2 = 50^2 - x^2 and that h^2 = 70^2 - (80 -x)^2
Both equations = h^2 so we can make a new equation
50^2 - x^2 = 70^2 - (80 -x)^2 which equals
2,500 -x^2 = 4,900 -6400 +160x -x^2
4,000 -x^2 = 160x -x^2
-2x^2 -160x +4,000 = 0