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

Jun 4, 2015

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.

Jun 4, 2015

This is an isosceles right triangle, in which both legs have the same length. In an isosceles right triangle, the hypotenuse is $\text{L} \sqrt{2}$, where $\text{L}$ is the length of a leg. So, since the length of the hypotenuse is $15 \sqrt{2}$, 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.

${c}^{2} = {a}^{2} + {b}^{2}$ =

${\left(15 \sqrt{2}\right)}^{2} = {15}^{2} + {15}^{2}$

$450 = 450$