JAMB Mathematics 2018 Paper

Concept:The two triangles are similar because they share two equal angles, so their corresponding sides are proportional.Explanation:Given that $\angle XMN = \angle XZY$ and $\angle X$ is common to both $\triangle XMN$ and $\triangle XZY$, the triangles are similar by AA similarity.Hence, $\triangle XMN \sim \triangle XZY$.So, the corresponding sides are in the same ratio:$$\frac{XM}{XZ} = \frac{XN}{XY}$$From the figure, $XM = 8$ cm, $XN = 12$ cm, and $NZ = 4$ cm.Thus, $XZ = XN + NZ = 12 + 4 = 16$ cm.Also, $XY = XM + YM = 8 + YM$.Substituting into the ratio equation:$$\frac{8}{16} = \frac{12}{8 + YM}$$Cross multiply:$$8(8 + YM) = 16 \times 12$$$$64 + 8YM = 192$$$$8YM = 192 - 64 = 128$$$$YM = \frac{128}{8} = 16 \text{ cm}$$Answer:$YM = 16$ cm, which is Option C.