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1 December, 00:28

One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find these lengths.

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  1. 1 December, 00:57
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    24m and 25m.

    Step-by-step explanation:

    By Pythagoras Theorem:

    h^2 = x^2 + 7 ^2 where h is the hypotenuse and x is the other leg.

    But x and h are consecutive integers

    so h = x + 1 and:

    (x + 1) ^2 = x^2 + 49

    x^2 + 2x + 1 - x^2 = 49

    2x + 1 = 49

    2x = 48

    x = 24

    So the 2 lengths are 24 and 25.
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