Find the value of the variable. leave in simplest radical form.

If the hypotenuse is equal to 11, then we can plug it into the Pythagorean theorem. So we get a^2+x^2=121. So we take the square root of both sides, sqrt(a^2+x^2)=11. So we take a^2 and x^2 out of the square root. We get a+x=11. So now we have two equations, a+x=11 and a^2+x^2=121. I’ll leave the rest of solving equations to you.

Hint: a=11-x
You can plug that into a^2+x^2=121