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16 October, 22:31

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

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  1. 17 October, 00:50
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    Let's make an equation based off of the pythagorean theorem.

    7²+x² = (x+1) ²

    Since the diagonal is the biggest of the three lengths, the diagonal is the bigger even number. Since they are consecutive, they are one away. Let's distribute.

    49+x²=x²+2x+1; let's subtract 1 from both sides.

    48+x²=x²+2x; lets subtract x² from both sides.

    48=2x; let's divide.

    48:2=24=x

    So, since smaller integer is 24, the bigger one is 25. Let's make sure this makes sense.

    7²+24²=25²

    49+576=625

    625=625

    So, the missing lengths are 24 and 25.
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