9. A large rectangle is divided into four identical smaller rectangles by slicing parallel to one of its sides. The perimeter of the large rectangle is 18 metres more than the perimeter of each of the smaller rectangles. The area of the large rectangle is $18 \mathrm{~m}^{2}$ more than the area of each of the smaller rectangles. What is the perimeter in metres of the large rectangle?
9. 28 Let the length of the original rectangle be $x$ metres and let the height be $y$ metres. Without losing any generality, assume the rectangle is sliced parallel to the height, as shown.
The information in the question tells us that $2 x+2 y=2\left(\frac{x}{4}\right)+2 y+18$ and that $x y=\left(\frac{x}{4}\right) y+18$. From the first equation, we have $\frac{3 x}{2}=18$ which has solution $x=12$. Substitute this value into the second equation to obtain $12 y=3 y+18$, which has solution $y=2$. Hence the perimeter of the large rectangle in metres is $2 \times 12+2 \times 2=28$.