5. Six rectangles are arranged as shown. The number inside each rectangle gives the area, in $\mathrm{cm}^{2}$, of that rectangle. The rectangle on the top left has height $6 \mathrm{~cm}$.
What is the height of the bottom right rectangle?
A $4 \mathrm{~cm}$
B $5 \mathrm{~cm}$
C $6 \mathrm{~cm}$
D $7.5 \mathrm{~cm}$
E $10 \mathrm{~cm}$
SolUtion
B

To obtain an area of $18 \mathrm{~cm}^{2}$, the width of the top left rectangle must be $(18 \div 6) \mathrm{cm}=3 \mathrm{~cm}$. Then the bottom left rectangle must have height $(12 \div 3) \mathrm{cm}=4 \mathrm{~cm}$. Similarly the bottom middle rectangle must have width $(16 \div 4) \mathrm{cm}=4 \mathrm{~cm}$, the top middle rectangle must have height $(32 \div 4) \mathrm{cm}=8 \mathrm{~cm}$, the top right rectangle must have width $(48 \div 8) \mathrm{cm}=6 \mathrm{~cm}$ and the bottom right rectangle must have height $(30 \div 6) \mathrm{cm}=5 \mathrm{~cm}$.