Calculate the Legs of a Right Isosceles Triangle: Finding Equal Side Lengths

In a right triangle, isosceles means the two legs (not the hypotenuse) are equal in length. The two acute angles are also both 45°.

In a 45-45-90 triangle, if each leg is length x, then the hypotenuse is always $x\sqrt{2}$. This comes from the Pythagorean theorem: $x^2 + x^2 = (x\sqrt{2})^2$.

The legs are the two sides that form the right angle (90°). The hypotenuse is always the longest side, opposite the right angle.

You can, but $\sqrt{64} = 8$ is a perfect square you should memorize! Knowing perfect squares like 36, 49, 64, 81, 100 makes geometry much faster.

Double-check your setup: Did you use $2AC^2 = (8\sqrt{2})^2$? Remember that $(8\sqrt{2})^2 = 64 \times 2 = 128$, so $AC^2 = 64$.