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3 May, 08:08

The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in. 2, which equation could be used to find the base (b) of the sign?

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  1. 3 May, 11:19
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    We should try the very simplest way of finding triangular areas first.

    Formula

    A = 1/2 b * h

    Substitute

    Area = 60 in^2

    b = x

    h = 2x - 1

    60 = 1/2 * x * (2x - 1)

    Solve

    60 = 1/2 * x (2x - 1) Multiply by 2

    60 * 2 = x (2x - 1)

    120 = x (2x - 1) Remove the brackets.

    120 = 2x^2 - x Subtract 120 from both sides.

    2x^2 - x - 120 = 0 This factors.

    (2x + 15) (x - 8) = 0

    Solve for x

    2x + 15 = 0

    2x = - 15

    x = - 15/2

    x = - 7.5 a negative measurement is useless. Discard this answer.

    x - 8 = 0

    x = 8

    Area (Check)

    base = 8

    height = 16 - 1 = 15

    Area = 1/2 * 8 * 15 = 60 as it should

    Answer

    Use Area = 1/2 * b * h to find the base and the height.
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