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

Base = x + 9

height = x

Area = 1/2 · b · h

180 = 1/2 (x + 9) (x)

180 = (x² + 9x) / 2

360 = x² + 9x

0 = x² + 9x - 360

Use Quadratic Formula to solve:

x = (-b + / - √b² - 4ac) / (2a)

= (-9 + / - √9² - 4·1·-360) / (2·1)

= (-9 + / - √9² + 1440) / (2)

= (-9 + / - √1449) / (2)

= (-9 + / - 38) / (2)

= (-9 + 38) / (2), (-9 - 38) / (2)

= 29/2, - 47/2

= 14.5, - 23.5

length cannot be negative! so disregard the - 23.5

Answer: The height of the triangle is 14.5 ft and the base is 14.5 + 9 = 23.5 ft

Area of a triangle = (1/2) * base*height

height = x

base = x+9

Area = (1/2) * (x+9) * x

180 = (1/2) * (x+9) * x

360 = (x+9) * x

x²+9x-360 = 0

a=1, b=9, c=-360

D=b²-4ac=81+4*360=1521, √D=√1521=39

x = (-b+/-√D) / 2a

x = (-9+/-39) / 2

We need only positive solution,

x = (-9+39) / 2

x=15 height

x+9=15+9=24 base

Height - 15 ft, base - 24 feet.