CDS 2026 (I) Elementary Mathematics, question 56

Topic: Geometry

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Q56

ABC is a triangle right-angled at B. Points M and N trisect BC. If AM=6AM=6 cm and AN=9AN=9 cm, then what is AC equal to ?

  1. (a) 4394\sqrt{39} cm
  2. (b) 2392\sqrt{39} cmCorrect answer
  3. (c) 24 cm
  4. (d) 20 cm

Solution.

Answer: (b) 2392\sqrt{39} cm

  1. Let BM=MN=NC=tBM = MN = NC = t and AB=aAB = a.
  2. The given lengths give a2+t2=36a^{2} + t^{2} = 36 and a2+4t2=81a^{2} + 4t^{2} = 81.
  3. Subtracting gives t2=15t^{2} = 15, then a2=21a^{2} = 21.
  4. Therefore AC2=a2+9t2=21+135=156AC^{2} = a^{2} + 9t^{2} = 21 + 135 = 156.