[tex]6\sqrt2[/tex]
Why?
We have the isosceles right triangle. The length of legs are 6. Use the Pythagorean theorem:
[tex]h^2=6^2+6^2\\\\h^2=36+36\\\\h^2=36\cdot2\to h=\sqrt{36\cdot2}\\\\h=\sqrt{36}\cdot\sqrt2\\\\h=6\sqrt2[/tex]
In general, the formula for calculating the hypotenuse in an isosceles right triangle is [tex]h=a\sqrt2[/tex]
a - a leg, h - a hypotenuse
