Since we have a right isosceles triangle,we have the following:
using the pythagorean theorem, we have:
[tex]\begin{gathered} x^2+x^2=(12)^2 \\ \Rightarrow2x^2=144 \\ \Rightarrow x^2=\frac{144}{2}=72 \\ \Rightarrow x=\sqrt[]{72}=6\cdot\sqrt[]{2} \\ x=6\cdot\sqrt[]{2} \end{gathered}[/tex]
therefore, the length of each leg of the isosceles right triangle is 6*sqrt(2)
