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28 July, 23:14

The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?

A. 5x2 - 2x - 24 = 0

B. 5x2 - 2x - 6 = 0

C. 5x2 - 2x - 12 = 0

D. 25x2 - 10x - 24 = 0

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Answers (2)
  1. 28 July, 23:50
    0
    C. 5x^2 - 2x - 24 = 0
  2. 29 July, 00:34
    0
    A. 5x^2 - 2x - 24 = 0

    Step-by-step explanation:

    height = 5b-2

    b = x

    We can rewrite the height as

    h = 5x-2

    We know the formula for area of a triangle

    A = 1/2 bh

    A = 1/2 x * (5x-2)

    Distributing the x

    A = 1/2 (5x^2 - 2x)

    We know A = 12

    12 = 1/2 (5x^2 - 2x)

    Multiply each side by 2

    12*2 = 2*1/2 (5x^2 - 2x)

    24 = 5x^2 - 2x

    Subtract 24 from each side

    24-24 = 5x^2 - 2x-24

    0 = 5x^2 - 2x-24
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