Algebra

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The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base.

  • Algebra -

    Area of triangle = 1/2(height x base)
    The problem states that base is 8 cm greater than the height; therefore, base-8 = height.
    A = 1/2(b*h)
    42 = 1/2(b*[b-8])
    84=(b^2-8b)
    rearrange to
    b^2 - 8b -84
    factor to
    (b+8)(b-14)
    Therefore, b = -8 cm which makes no sense and
    b = +14 cm
    and height = 14-8 = 6
    Check:
    1/2(b*h) = area
    1/2(14*6) = 1/2(84)=42
    Check my work.

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