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11 December, 09:02

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long should the sides of the triangle be?

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  1. 11 December, 09:31
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    18cm, 24cm, 30cm

    Step-by-step explanation:

    Let x be the length of the shorter leg

    (x + 12) ² = (x + 6) ² + x²

    x² + 24x + 144 = x² + 12x + 36 + x²

    x² - 12x - 108 = 0

    x² - 18x + 6x - 108 = 0

    x (x - 18) + 6 (x - 18) = 0

    (x - 18) (x + 6) = 0

    x = 18, - 6

    x = 18

    x + 6 = 24

    x + 12 = 30
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