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13 August, 04:51

If the base of a triangle is 4 units longer than twice its height and has an area of 240 square units, how long is the base of the triangle?

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  1. 13 August, 07:26
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    The area of the triangle is:

    A = (1/2) * (b) * (h)

    Where,

    b: base

    h: height

    Substituting values we have:

    Where,

    b = 2h + 4

    h = (1/2) * b-2

    Substituting values we have:

    240 = (1/2) * (b) * ((1/2) * b-2)

    Rewriting:

    480 = ((1/2) * b ^ 2-2b)

    960 = b ^ 2-4b

    b ^ 2-4b-960 = 0

    Solving the polynomial:

    b1 = 22.93171219946131

    b2 = - 20.93171219946131

    Using the positive root we have:

    b = 22.9 units

    Answer:

    the base of the triangle is:

    b = 22.9 units
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