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WAEC Mathematics 2008 Question 24

Question 24

Mensuration of Plane Shapes

In the figure |PX| = |XQ|, PQ // YZ and XY // QR. What is the ratio of the area of XYZQ to the area of ΔYZR?

Diagram for this question
  1. A.1:2
  2. B.2:1
  3. C.1:3
  4. D.3:1
Show the answer and explanation

Answer: B (2:1)

Explanation

X is the midpoint of PQ, so Y and Z are midpoints of PR and QR (midpoint theorem). The triangle splits into four equal triangles: XYZQ is two of them and YZR is one, so the ratio is 2 : 1.