Answer:
[tex]6\sqrt{5}[/tex]
Step-by-step explanation:
In any right triangle, the Pythagorean theorem states:
[tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.
Plugging in given values, we have:
[tex]12^2+VU^2=18^2,\\144+VU^2=324,\\VU^2=180,VU=\sqrt{180}=\sqrt{36}\cdot \sqrt{5}=\boxed{6\sqrt{5}}[/tex]
