Intermediate Algebra

One leg of a right triangle has a length of 5 m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is ____ m

The length of the hypotenuse is ____ m

Is my answer correct?

The other leg is 12 m
The hypotenuse is 13 m

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  1. Correct

    The other sides :

    x

    and

    x + 1

    where x + 1 is the hypotenuse

    So Pythagorean theorem:

    ( x + 1 ) ^ 2 = x ^ 2 + 5 ^ 2

    x ^ 2 + 2 x + 1 = x ^ 2 + 25 Both x ^ 2 get cancelled

    2 x + 1 = 25

    2 x = 25 - 1 = 25 - 1 = 24

    x = 24 / 2 = 12 m

    hypotenuse

    x + 1 = 12 + 1 = 13 m

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  2. It is 12

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  3. Hypo is 13

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