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The base of a triangle is 3 cm greater than the height. The area is 14cm^2. Find the length and height of the base.

  • math - ,

    The area of a triangle is
    A = base * height /2

    If you have not learned to solve quadratic equations before, then think of
    2A = base * height
    Since A=14, 2A = 28
    Look for two integers that multiply together to give 28, but with a difference of 3 between them.

    If you have learned quadratic equations, then let
    b=base = h+3

    Using the area formula above, you'll get
    A=14 = h(h+3)/2
    from which you can solve for the height h. The base is simply h+3.

  • math - ,

    let the height be x cm
    then the base is x+3 cm

    x(x+3)/2 = 14

    solve for x

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