24. Three congruent squares overlap as shown. The area of the three overlapping sections are $2 \mathrm{~cm}^{2}, 5 \mathrm{~cm}^{2}$ and $8 \mathrm{~cm}^{2}$ respectively. The total area of the non-overlapping parts of the square is $117 \mathrm{~cm}^{2}$.
What is the side-length of each square?
A $6 \mathrm{~cm}$
B $7 \mathrm{~cm}$
E $8 \mathrm{~cm}$
D $9 \mathrm{~cm}$
E $10 \mathrm{~cm}$
Solution: B
The total area of the three squares is the sum of area of the non-overlapping parts and twice the areas of the overlapping sections as each of these forms part of two squares. So the total area of the squares is, in $\mathrm{cm}^{2}, 117+2 \times(2+5+8)=117+2 \times 15=117+30=147$. Hence the area of one of the squares is one third of this, that is, $49 \mathrm{~cm}^{2}$. Therefore the side-length of each square is $7 \mathrm{~cm}$.