GCE Mathematics 2024 Objective — Question 21

Question 21 of 50 from the General Certificate of Education (GCE) 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.

Sign up free to unlock

Score tracking
Practice history
Saved questions
Progress dashboard
Personalized sessions
Weak-topic breakdown

…and/or go further with premium services and No Ads.

Create free account

More questions from Mathematics 2024 Objective More Mathematics past papers