Triangles

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Right traingles C and D share a leg. If the ratio of the area of traingle C to the area of traingle D is 5:9, C’s hypotenuse is of length 25, and D’s hypotenuse is of length 39, what is the area of C?

  • Triangles -

    For the non-shared legs,
    let the shorter be x and the longer be y

    let the length of the shared leg be h
    so x^2 + h^2 = 25^2 and y^2 + h^2 = 39^2
    h^2 = 625-x^2 and h^2 = 1521 - y^2

    625 - x^2 = 1521 - y^2
    y^2 - x^2 = 896

    Also, (1/2)xh /(1/2)yh = 5/9
    x/y = 5/9
    9x = 5y
    x = 5y/9

    y^2 - 25y^2/81 = 896
    times 81
    81y^2 - 25y^2 = 72576
    56y^2 = 72576
    y^2 = 1296
    y = ± 36 , rejecting the negative, since we can't have a negative length of a line

    y= 36, then in x=5y/9 -------->

    take it from here

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