# math

One leg of a right triangle has a length of 15 m. The other sides have lengths that are consecutive integers. Find the number of meters in the perimeter.

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1. (n+1)^2 = 225 + n^2
n^2 + 2 n + 1 = 225 + n^2
2 n = 224 etc

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2. 15^2 + x^2 = (x+1)^2
225 + x^2 = x^2 + 2n + 1
225 = 2n + 1
224 = 2n
112 = n

So the three sides have a length of 15, 112, and 113 which gives us a perimeter of 240

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