algebra

The base of a triangle is 8 cm greater than the height. The area is 64 cm^2. Find the height and the length of the base.

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  1. height = X-cm,
    Base = (X + 8)cm,

    A = bh/2 = (X + 8)X/2 = 64,
    Multiply both sides by 2:
    (X + 8)X = 128,
    X^2 + 8X = 128,
    X^2 + 8X - 128 = 0,
    (X - 8)(X + 16) = 0,

    X - 8 = 0,
    X = 8.

    X + 16 = 0,
    X = -16.

    Use the + value of X:
    X = 8cm = height.
    X + 8 = 8 + 8 = 16cm = base.

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