15. A flag is in the shape of a right-angled triangle, as shown, with the horizontal and vertical sides being of length $72 \mathrm{~cm}$ and $24 \mathrm{~cm}$ respectively. The flag is divided into 6 vertical stripes of equal width.
What, in $\mathrm{cm}^{2}$, is the difference between the areas of any two adjacent stripes?

A 96
B 72
C 48
D 32
E 24
15. C The stripes are of equal width, so the width of each stripe is $(72 \div 6) \mathrm{cm}=$ $12 \mathrm{~cm}$. The diagram shows that the difference between the areas of any two
adjacent stripes is equal to the area of a rectangle of width $12 \mathrm{~cm}$ and height $h \mathrm{~cm}$. By similar triangles, $\frac{h}{12}=\frac{24}{72}$. So $h=\frac{12 \times 24}{72}=4$. So the required area is $12 \times 4 \mathrm{~cm}^{2}=48 \mathrm{~cm}^{2}$.