Question 21
Mensuration of Plane ShapesIn the diagram, MN // KL, ML and KN intersect at X. |MN| = 12 cm, |MX| = 10 cm and |KL| = 9 cm. If the area of ΔMXN is 16 cm2, calculate the area of ΔLXK.
- A.8 cm2
- B.9 cm2
- C.10 cm2
- D.12 cm2
Show the answer and explanation
Answer: B (9 cm2)
Explanation
Because MN // KL, triangles MXN and LXK are similar with scale factor 9/12 = 3/4. Areas scale by (3/4)² = 9/16, so the area is 16 × 9/16 = 9 cm².