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

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