Test Index

WAEC Mathematics 2024 Paper

Question : 21

Total: 50

In the diagram above, $\overline{MN} \parallel \overline{KL}$ , $\overline{ML}$ and $\overline{KN}$ intersect at X. | $\overline{MN}$ | = 12cm, | $\overline{MX}$ | = 10cm and | $\overline{MN}$ | = 9cm. If the area of $\triangle$ MXN is 16cm $^2$ , calculate the area of $\triangle$ LXK

9cm $^2$
8cm $^2$
10cm $^2$
12cm $^2$

Validate

Solution:

$\overline{MN} \parallel \overline{KL}$ , $\triangle$ LXK is similar to $\triangle$ MXN

So, the ratio of the areas of the two similar triangles equals the square of the ratio of their corresponding sides

Therefore, $\frac{\text{Area of }\triangle MXN}{\text{Area of }\triangle LXK} = \frac{12^2}{9^2}$

$\frac{16}{\text{Area of }\triangle LXK} = \frac{144}{81}$

Area of $\triangle$ LXK = $\frac{16 \times 81}{144} = 9\,\text{cm}^2$

Go to Question:

Prev Question

Next Question