8. A circle with radius $x \mathrm{~cm}$ is inscribed inside a triangle $\mathrm{ABC}$, where $\angle \mathrm{ACB}$ is a right angle. If $\mathrm{AB}=9 \mathrm{~cm}$ and the area of the triangle $\mathrm{ABC}$ is $36 \mathrm{~cm}^{2}$, find the value of $x$.
(A) 2.2
(B) 2.6
(C) 3
(D) 3.4
(E) 3.8
8. Answer: (C)

Note that area of $\triangle \mathrm{ABC}=(\mathrm{AB}) x+x^{2}$. Thus we obtain $36=9 x+x^{2}$, or $x^{2}+9 x-36=0$. Solving the equation gives $x=3$ or $x=-12$, so the radius is $3 \mathrm{~cm}$.