# An isosceles right triangle has perimeter 36, what are the sides

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The perimeter of a right isosceles triangle is 36. Let the length of the equal side be x. The length of the hypotenuse is 36 - 2x.

The Pythagorean Theorem gives `x^2 + x^2 = (36 - 2x)^2`

=> `2x^2 = 1296 - 144x + 4x^2`

=> `2x^2 - 144x + 1296 = 0`

=> `x^2 - 72x + 648 = 0`

`x = (72 +-sqrt 2592)/2`

= `36 +- 18*sqrt 2`

The length of the hypotenuse is `-36 +- 36*sqrt 2`

Ignore the root `36 + 18*sqrt 2` as it gives a negative value for the length of the hypotenuse.

**The length of the sides of the triangle is `{36 - 18*sqrt 2, 36 - 18*sqrt 2, -36 + 36*sqrt 2}` **