right triangles

## 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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# 2 Answers

You know by the Pythagorean theorem that a^{2} +b^{2} = c^{2} 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:

7^{2} + b^{2} = (b+1)^{2}

FOIL the b+1 and get all the b's on one side (b^{2} will cancel since you have +1b^{2} 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.

Do you know the Pythagorean triple: 7-24-25?

Answer: The other two sides are 24 cm and 25 cm.