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

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The two other points would be 5 m. and 3 m.

When they say the other 2 sides are consecutive integers then --> x = x + 1 , where 'x + 1' is the hypotenuse.

(x + 1)² = x² + 5²

x² + 2x + 1 = x² + 25 --> Both x² get cancelled.

2x + 1 = 25 ---> 2x = 24 ---> x = 12

The other leg is 12 m

The hypotenuse is 13 m hope this helped you.