26. In the diagram below, $A$ and $B(20,0)$ lie on the $x$-axis and $C(0,30)$ lies on the $y$-axis such that $\angle A C B=90^{\circ}$. A rectangle $D E F G$ is inscribed in triangle $A B C$. Given that the area of triangle $C G F$ is 351 , calculate the area of the rectangle $D E F G$.
26. Answer: 468 .
Note that $A O=\frac{30^{2}}{20}=45$. Then the area of $\triangle A B C$ is $\frac{(20+45) \times 30}{2}=975$.
Let the height of $\triangle C G F$ be $h$. Then
$$
\left(\frac{h}{30}\right)^{2}=\frac{351}{975}=\left(\frac{3}{5}\right)^{2} \Rightarrow \frac{h}{30-h}=\frac{3}{2}
$$

Note that the rectangle $D E F G$ has the same base as $\triangle C G F$. Then its area is
$$
351 \times \frac{2}{3} \times 2=468
$$