NECO Mathematics 2024 Objective — Question 21

Question 21 of 50 from the National Examinations Council (NECO) Mathematics 2024 Objective paper, with the correct answer and a full explanation.

In the diagram, MN//KL, ML and KN intersect at X. |MN|=12cm, |MX|=10cm and |KL|=9cm. If the area of ΔMXV is 16cm², calculate the area of ΔLXK.

A. A. 8cm²
B. B. 9cm²Correct
C. C. 10cm²
D. D. 12cm²

Explanation

Since MN//KL, triangles MXN and LXK are similar (AA similarity), with the ratio of corresponding sides MN:KL=12:9=4:3. The ratio of areas of similar triangles equals the square of the ratio of corresponding sides: (4/3)²=16/9. Since area of ΔMXN=16cm², area of ΔLXK = 16×(9/16) = 9cm².

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