BECE Mathematics 2013 Paper

Concept:Similar figures have corresponding sides in the same ratio, called the scale factor.Explanation:The two figures $ABCD$ and $PQRS$ are similar, so each side of $PQRS$ is obtained by multiplying the corresponding side of $ABCD$ by the same scale factor.From the given pairs of corresponding sides, the scale factor is:$\frac{10}{6} = \frac{20}{12} = \frac{15}{9}$Notice that $\frac{15}{9} = \frac{5}{3}$, so the scale factor is $\frac{5}{3}$.The side $b$ in figure $PQRS$ corresponds to the side $18$ in figure $ABCD$.Thus, $\frac{b}{18} = \frac{15}{9}$.Cross multiplying gives:$b \times 9 = 15 \times 18$$9b = 270$Divide both sides by $9$:$b = \frac{270}{9} = 30$So the length of side $b$ is $30$ cm.Answer:$b = 30$ cm, which is option D.