22. A rectangle with integer side-lengths is divided into four smaller rectangles, as shown. The perimeters of the largest and smallest of these smaller rectangles are $28 \mathrm{~cm}$ and $12 \mathrm{~cm}$.
Which of the following is a possible area of the original rectangle?

A $90 \mathrm{~cm}^{2}$
B $92 \mathrm{~cm}^{2}$
C $94 \mathrm{~cm}^{2}$
D $96 \mathrm{~cm}^{2}$
E $98 \mathrm{~cm}^{2}$
22. D Let the largest rectangle measure $p \mathrm{~cm}$ by $q \mathrm{~cm}$ and the smallest rectangle measure $r \mathrm{~cm}$ by $s \mathrm{~cm}$, as shown.
Then $2 p+2 q=28$ and $2 r+2 s=12$.
Now the perimeter, in $\mathrm{cm}$, of the original rectangle
is $2 p+2 q+2 r+2 s=28+12=40$.
Hence $p+q+r+s=(p+s)+(q+r)=20$.

So the length and width, in $\mathrm{cm}$, of the original rectangle sum to 20 .
The area of the original rectangle is the product of its width and length. Of options given, only an area of $96 \mathrm{~cm}^{2}$ gives a possible width and length which sum to $20 \mathrm{~cm}$, namely $8 \mathrm{~cm}$ and $12 \mathrm{~cm}$. (It is left to the reader to show that none of the other four options corresponds to integer values for the width and length which sum to $20 \mathrm{~cm}$. )