16. A rectangular thin wooden board, 7 meters long and 5 meters wide, has a small rectangular area at one corner damaged by insects, the damaged part is 2 meters long and 1 meter wide. Please design a method to saw off the damaged area in one straight cut, making the area removed as small as possible. What is the minimum area to be removed? Explain your reasoning.
【Answer】4 square meters
【Solution】As shown in the figure, let $MG=x, EN=y$
Obviously, $\triangle MGF \sim \triangle FEN$, so: $\frac{x}{2}=\frac{1}{y} \Rightarrow xy=2$
$S_{\triangle MGF}=\frac{x}{2}, \quad S_{\triangle AE:}=y$
Find the minimum value of $\frac{x}{2}+y$
$\frac{x}{2}+\frac{2}{x} \leq 2 \times \frac{x}{2}+\frac{2}{x}=2$
$\therefore \frac{x}{2}+y$ minimum value is 2.
The minimum area is: $2+1 \times 2=4\left(\mathrm{~m}^{2}\right)$.