The base of a triangle exceeds its height by 17 inches. if its area is 55 square inches, find the base and height of the triangle

Let h = height. This makes the base h + 17.

h (h + 17) / 2 = 55

h (h + 17) = 110

h^2 + 17h = 110

h^2 + 17h - 110 = 0

(h + 22) (h - 5) = 0

h = - 22 or h = 5

Discard h = - 22 because a negative height makes no sense, leaving just

h = 5in

base = 5 + 17 = 22in