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15 December, 03:14

The legs of a right triangle have lengths of 28 meters and 21 meters. the hypotenuse has a length of 5x meters. what is the value of x?

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  1. 15 December, 03:35
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    We have a right triangle with

    a = one leg = 28

    b = other leg = 21

    c = hypotenuse = 5x

    use the pythagorean theorem (a^2+b^2 = c^2) and solve for x

    a^2+b^2 = c^2

    28^2+21^2 = (5x) ^2

    784+441 = 25x^2

    1225 = 25x^2

    25x^2 = 1225

    (25x^2) / 25 = 1225/25

    x^2 = 49

    sqrt (x^2) = sqrt (49)

    |x| = 7

    x = 7 or x = - 7

    Since the hypotenuse has length 5x meters, this means

    5x = 5*7 = 35

    or

    5x = 5 (-7) = - 35

    Toss out the negative length as it makes no sense.

    The only value of x is x = 7

    Therefore the final answer is x = 7
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