BECE Mathematics 2013 Paper

Since the two figures are similar, figure $P Q R S$ is an enlargement of figure $A B C D$.During an enlargement, each side is being multiplied by the same scale factor.You can use any of the given sides to find the scale factor and use it to find the side of $b$.$\;\text{Scale factor}\;=\;\frac{\;\text{Image Size of similar side}\;}{\;\text{Object Size of similar side}\;}$The scale factor is the same for all similar sides.$\;\text{Scale factor}\;=\;\frac{10}{6}=\;\frac{20}{12}=\;\frac{15}{9}=\;\frac{b}{18}$ Using any of the fractions to the left of $\;\frac{b}{18}$, you can solve for the value of $b$ by equating it to any of the fractions at the left since they are all the same.$\;\frac{15}{9}=\;\frac{b}{18}$Cross multiply.$b \times 9 = 15 \times 18$Divide both sides by 9$b = \;\frac{15 \times 18}{9} = 15 \times 2 = 30 \text{ cm}$Note: 9 divides itself once and 18, 2 times.