SOLUTION: the base of a triangle exceeds the height by 9 centimeters. if the area is 161 square centimeters, find the length of the bas and the height of the triangle.

Question 839745: the base of a triangle exceeds the height by 9 centimeters. if the area is 161 square centimeters, find the length of the bas and the height of the triangle.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
let b = base
h = height
b = h + 9
area = (1/2)(b)(h)
substituting
area = (1/2)(h + 9)(h)
161 = (1/2)(h + 9)(h)
161 = (1/2)(h^2 + 9h)
multiply each side by 2
322 = h^2 + 9h
add -322 to each side
0 = h^2 + 9h - 322
0 = (h+23)(h-14)
h = -23 or h = 14
Since we need a positive length we want h = 14
Since b = h + 9
b = 14 + 9 = 23
The base is 23 and height is 14

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