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30 April, 06:10

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.

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Answers (2)
  1. 30 April, 09:53
    0
    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
  2. 30 April, 10:03
    0
    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.
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