Question

In a 45° - 45° - 90° right triangle, the length of the hypotenuse is `15sqrt2`, what is the length on one of the legs?

Answer 1

Call a the side and c the hypotenuse
Use the right triangle rule: a^2 + a^2 = c^2

2a^2 = 2(225) = 450 -> a^2 = 225 -> a = 15.

Answer 2

This is an isosceles right triangle, in which both legs have the same length. In an isosceles right triangle, the hypotenuse is `"L"sqrt2`, where `"L"` is the length of a leg. So, since the length of the hypotenuse is `15sqrt2`, one of the legs (both legs, actually) is `15`.
http://www.regentsprep.org/regents/math/algtrig/att2/ltri45.htm

We can prove this with the Pythagorean theorem.

`c^2=a^2+b^2` =

`(15sqrt2)^2=15^2+15^2`

`450=450`