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State PCS PYQPrelims 2024

BPSC – Combined Competitive Examination · Question 52

How many triangles are there in figure PQRS? (Figure: rectangle PQRS with both diagonals meeting at centre O, plus one horizontal segment from the left side to O and one vertical segment from O down to the bottom side.)

  1. 16
  2. 10
  3. 18
  4. 12
Show answer & explanation

Answer: (D) 12

Explanation

Diagonals of a rectangle form 8 triangles; two centre-to-side segments each add 2 more, giving 12.

  • (A) Incorrect

    Wrong: overcounts; the extra segments add only 4 triangles.

  • (B) Incorrect

    Wrong: undercounts the triangles made by the extra segments.

  • (C) Incorrect

    Wrong: overcounts.

  • (D) Correct

    Correct: diagonals give 8 triangles (4 small + 4 large); each extra segment splits one small triangle into 2, adding 4: total 12.