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Math Help - Isoscoles Triangle Problem

  1. #1
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    Isoscoles Triangle Problem

    Sorry, I think I posted this in the wrong thread, so here it is again. My apologies for the double post.

    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
    MHF Contributor
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    Let h = height of triangle (from vertex to side x)
    Draw that height line: you'll end up with 2 right triangles sides 8, x/2 and h ; ok?

    So (pythagorean theorem): h^2 + x^2/4 = 64 [1]

    Area = height * base / 2
    So hx/2 = 24 ; hx = 48 ; h = 48/x [2]

    Substitute [2] in [1]:
    (48/x)^2 + x^2/4 = 64

    Solve for x
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