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

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You know by the Pythagorean theorem that a2 +b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse or longest side. When they say the other two legs are consecutive integers, that means that x = x+1 or in this case c = b+1. By substituting c = b+1 and 7cm into the Pythagorean theorem, you will get:

72 + b2 = (b+1)2

FOIL the b+1 and get all the b's on one side (b2 will cancel since you have +1b2 on both sides). You should be able to solve for b. Then, use that value to get c since you know c = b+1. Check it by plugging your values back into the Pythagorean theorem.