The base of a triangle exceeds the height by 4 inches. if the area is 178.5 square inches, find the length of the base and the height of the triangle.

A = 1/2 * b * h

A = 178.5

b = h + 4

178.5 = 1/2 * (h + 4) * h

357 = h^2 + 4h

h^2 + 4h - 357 = 0

(h - 17) (h + 21) = 0

h - 17 = 0

h = 17

h + 21 = 0

h = - 21 ... not this one because it is negative

b = h + 4

b = 17 + 4

b = 21

so the height is 17 inches and the base is 21 inches <==