If the hypotenuse of a 45-45-90 triangle is 13, what is the length of the legs?

The legs of this triangle are each of length 1 unit as they are both original sides of the unit square. That is, the legs of this 45-45-90 triangle are equal. Applying the Pythagorean theorem we find that the length of the hypotenuse is equal to the square root of 2.