Question

The base of a triangle exceeds the height by 9 inches. If the area is 180 square inches, find the length of the base and the height of the triangle.

Answer 1

A=1/2bh
180=1/2(h+9)(h) Multiply through by 2 to get rid of fraction. Also distribute right side.
360=h^2+9h.
h^2+9h-360=0. Factor.
(h+24)(h-15)=0
So h=15 (can’t be a negative so not -24)

Since base is 9 more than height, b=24

So...h=15 inches and b=24 inches

Check: 1/2(15)(24)=15(12)=180