CDS 2026 (I) Elementary Mathematics, question 54

Topic: Geometry

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Q54

Let ABCD be a parallelogram and E be the midpoint of BC. The diagonal BD and line segment AE intersects at F. If BF=2.4BF=2.4 cm, then what is BD equal to ?

  1. (a) 6.06.0 cm
  2. (b) 6.46.4 cm
  3. (c) 7.27.2 cmCorrect answer
  4. (d) 8.48.4 cm

Solution.

Answer: (c) 7.27.2 cm

  1. Triangles EBF and ADF are similar: EB is parallel to AD, BF lies on DF, and EF lies on AF.
  2. Since E is the midpoint of BC and BC=AD,EB/AD=1/2BC = AD,EB/AD = 1/2.
  3. Thus BF/FD=1/2BF/FD = 1/2 and BD=BF+FD=3BF=3×2.4=7.2cmBD = BF + FD = 3BF = 3 \times 2.4 = 7.2cm.