18. The points $P, Q, R$ and $S$ are marked on a straight line in some order. The lengths of the line segments $P Q, Q R, R S$ and $S P$ are $13 \mathrm{~cm}, 11 \mathrm{~cm}, 14 \mathrm{~cm}$ and $12 \mathrm{~cm}$ respectively. What is the distance between the two points that are furthest apart?
A $14 \mathrm{~cm}$
B $25 \mathrm{~cm}$
C $27 \mathrm{~cm}$
D $38 \mathrm{~cm}$
E $50 \mathrm{~cm}$
18. B Let points $P$ and $Q$ be a distance $13 \mathrm{~cm}$ apart with $Q$ to the right of $P$ as shown.

The information in the question tells us that $Q R=11 \mathrm{~cm}$ but not which side of $Q$ the point $R$ is. Therefore either $P R=(13+11) \mathrm{cm}=24 \mathrm{~cm}$ or $P R=(13-11) \mathrm{cm}=2 \mathrm{~cm}$, giving two possible positions for $R$, marked as $R_{1}$ and $R_{2}$ on the diagram. In a similar way, since $R S=14 \mathrm{~cm}$, the distance $P S$ is then equal to $(24 \pm 14) \mathrm{cm}$ or $(14 \pm 2) \mathrm{cm}$. However, the question also tells us that $P S=12 \mathrm{~cm}$ and, of the possible distances, only $(14-2) \mathrm{cm}$ gives us a distance $12 \mathrm{~cm}$. Therefore $S$ is $14 \mathrm{~cm}$ to the left of $R_{1}$ and the two points furthest apart are $S$ and $Q$ at a distance $(12+13) \mathrm{cm}=25 \mathrm{~cm}$.