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Math Help - Can anyone solve this Isosceles triangle problem

  1. #1
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    Can anyone solve this Isosceles triangle problem

    A landscape designer uses 8-foot timbers to form a pattern of isosceles triangles along the wall of a building. If the area of each triangle is 24 square feet, and the two equal sides are 8 feet each, what is the base?

    So this is the problem:
    Side A = 8 feet
    Side B = 8 feet
    Side C = X
    Area = 24 square feet

    Could someone answer this and explain how the answer was found?
    I'm currently studying modeling with Linear and Quadratic Functions if that helps.
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  2. #2
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    Call the length of side C 2x, (= your X), and the heigth of the triangle y.
    Then, using the known area of the triangle, xy=24, and using the Pythagoras theorem x^2+y^2=64.
    Substitute for y in the second equation and then solve this as a quadratic in x^2.
    (I calculate x=3.2915, or x=7.2915,. But you should check these results.)
    (And remember to double them for the length of C.)
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