12. Maddie has a paper ribbon of length $36 \mathrm{~cm}$. She divides it into four rectangles of different lengths. She draws two lines joining the centres of two adjacent rectangles as shown.

What is the sum of the lengths of the lines that she draws?
12. A Let the lengths of the four rectangles be $p \mathrm{~cm}, q \mathrm{~cm}, r \mathrm{~cm}$ and $s \mathrm{~cm}$ with $p+q+r+s=36$. The lines Maddie draws join the centres of two pairs of rectangles and hence have total length $\left(\frac{1}{2} p+\frac{1}{2} q\right) \mathrm{cm}+\left(\frac{1}{2} r+\frac{1}{2} s\right) \mathrm{cm}=\frac{1}{2}(p+q+r+s) \mathrm{cm}$. Therefore the sum of the lengths of the lines she draws is $\frac{1}{2} \times 36 \mathrm{~cm}=18 \mathrm{~cm}$.