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3 September, 17:02

The base of a parallelogram is 18 inches longer than three times the height. The area of the parallelogram is 216 square inches. What is the height?

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  1. 3 September, 17:18
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    12 inches

    Step-by-step explanation:

    Let b represent the base

    h represents the height

    area of the parallelogram = base * height = 216 square inches

    From the question'

    b = 18 + 3h

    Slot in the value of b

    216 = (18 + 3h) * h

    expand

    216 = 18h + 3h^2

    subtract 216 from both sides

    0 = 18h + 3h^2 - 216

    rearrange

    3h^2 + 18h - 216 = 0

    divide through by 3

    h^2 + 6h - 72 = 0

    Now, lets solve!

    h^2 + 6h - 12h - 72 = 0

    h (h + 6) - 12 (h + 6) = 0

    (h - 12) (h + 6) = 0

    h - 12 = 0

    h = 12

    and

    h + 6 = 0

    h = - 6

    Taking the positive value of h

    Hence, the height is 12 inches

    Lets check

    when h = 12 inches

    Area of the parallelogram = 18 * 12 = 216 square inches ... correct

    when h = - 6inches

    A = 18 * - 6 ≠ 216 square inches

    So height is 12 inches
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