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A garden has the shape of a right triangle with one leg 3 meters longer tha the other. The hypotenuse is 3 meters less than twice the lenght of the shorter leg.

  • math -

    b = a + 3
    c = 2a -3
    c^2 = a^2 + b^2 (Pythagorean theorem)

    Solve those three equations simultaneously.

    c^2 = 4a^2 -12a +9
    c^2 = a^2 + (a+3)^2 = 2a^2 +6a +9

    2a^2 -18a =0
    a = 9
    b = 12
    c = 15

  • math -

    s^2 + l^2 = h^2

    s^2 + (s+3)^2 = (2s-3)^2

    s^2 + s^2 + 6 s + 9 = 4 s^2 - 12 s + 9

    2 s^2 - 18 s = 0 = 2s(s-9)

    s = 0 or s = 9
    the s = 0 root is irrelevant since that results in a negative hypotenuse

    s = 9
    l = 9+3 = 12
    h = 15

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