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WAEC Mathematics 1996 Question 33

Question 33

Triangles and Quadrilaterals

In the diagram, <PMN = <PRQ and <PNM = <PQR. If /PM/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/

Diagram for this question
  1. A.1cm
  2. B.3cm
  3. C.3½cm
  4. D.5cm
  5. E.6cm
Show the answer and explanation

Answer: A (1cm)

Explanation

Triangles PMN and PRQ are similar, with M matching R and N matching Q. So PM/PR = PN/PQ: 3/PR = 5/10, giving PR = 6 cm. NR = PR − PN = 6 − 5 = 1 cm.