2. A rectangle with perimeter $30 \mathrm{~cm}$ is divided by two lines, forming a square of area $9 \mathrm{~cm}^{2}$, as shown in the figure.
What is the perimeter of the shaded rectangle?
A $14 \mathrm{~cm}$
B $16 \mathrm{~cm}$
C $18 \mathrm{~cm}$
D $21 \mathrm{~cm}$
E $24 \mathrm{~cm}$
SolUTION
C

The square has sides of length $\sqrt{9} \mathrm{~cm}=3 \mathrm{~cm}$. Let $x$ and $y$ be the width and length in $\mathrm{cm}$ of the shaded rectangle. Then the large rectangle has perimeter $2(3+x+3+y)=30$. This gives $6+x+y=15$ so $x+y=9$. Hence the perimeter in $\mathrm{cm}$ of the shaded rectangle is $2(x+y)=2 \times 9=18$.