# 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

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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