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.

Answer 1

225 + x^2= (x+1)^2
225 + x^2 = x^2 + 2 x + 1
2 x = 224
x = 112
x+1 = 113
perimeter = 15 + 112 + 113

Answer 2

The other sides :

x and x + 1

where x + 1 is the hypotenuse

So Pythagorean theorem:

( x + 1 )² = x² + 15²

x² + 2 x + 1 = x² + 225

Both x² get cancelled

2 x + 1 = 225

2 x = 225 - 1 = 224

x = 224 / 2 = 112 m

Hypotenuse:

x + 1 = 112 + 1 = 113 m

Perimeter = 15 +112 + 113 = 240 m

Checking the solution:

112² + 15² = 12544 + 225 = 12769 = 113²