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9 July, 18:09

The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find the side lengths of the triangle

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  1. 9 July, 18:58
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    Longer leg = x + 4

    Shorter leg = x

    Hypotenuse = x + 8

    Using Pythagorean Theorem:

    a^2 + b^2 = c^2

    (x + 4) ^2 + x^2 = (x + 8) ^2

    x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

    2x^2 + 8x + 16 = x^2 + 16x + 64

    2x^2 + 8x = x^2 + 16x + 48

    2x^2 - 8x = x^2 + 48

    x^2 - 8x = 48

    x^2 - 8x - 48 = 0

    You can complete the square from here or use the quadratic formula.

    Completing the square:

    x^2 - 8x = 48

    x^2 - 8x + (-8/2) ^2 = 48 + (-8/2) ^2

    x^2 - 8x + 16 = 48 + 16

    (x - 4) (x - 4) = 64 or (x - 4) ^2 = 64

    x - 4 = + √64 OR x - 4 = - √64

    x - 4 = + 8 OR x - 4 = - 8

    x = 12 OR x = - 4

    However, you can't use negative 4 as a length because your length needs to be a positive.

    So x will be 12.

    Shorter leg: 12

    Longer leg: 12 + 4

    Hypotenuse: 12 + 8
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