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21 January, 05:50

The hypotenuse of a right triangle is 8 cm long. one leg is 2 cm longer than the other. find the length of the longer leg to the nearest tenth.

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  1. 21 January, 08:56
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    General formula to find the sides of right triangle is

    a² + b² = c²

    c stands for the hypotenuse

    We can assume a stands for the shorter leg and b is the longer leg, the equation will be

    b = a + 2

    a = b - 2

    Now input the number to the formula

    a² + b² = c²

    (b-2) ² + b² = 8²

    b² - 4b + 4 + b² = 64

    2b² - 4b + 4 - 64 = 0

    2b² - 4b - 60 = 0

    b² - 2b - 30 = 0

    Work the equation by completing the square

    b² - 2b - 30 = 0

    b² - 2b = 30

    b² - 2b + 1 = 30 + 1

    (b + 1) ² = 31

    b + 1 = √31

    b = - 1 + √31

    b = - 1 + 5.5678

    b = 4.5678

    b = 4.6

    The longer leg is approximately 4.6
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