imc

We let $a=\sqrt{49-x^2}+\sqrt{25-x^2}$; in other words, we want to find $a$. We know that $a\cdot 3=\left(\sqrt{49-x^2}+\sqrt{25-x^2}\right)\cdot \left(\sqrt{49-x^2}-\sqrt{25-x^2}\right)={\left(\sqrt{49-x^2}\right)}^2-{\left(\sqrt{25-x^2}\right)}^2=\left(49-x^2\right)-\left(25-x^2\right)=24.$ Thus, $a=\boxed{8}$.