Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 59

Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:<br/>1. It is possible to cut the sheet exactly into 4 square sheets.<br/>2. It is possible to cut the sheet into 10 triangular sheets of equal area.<br/><br/>Which of the above statements is/are correct?

  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer

Both 1 and 2

1. Possible to cut into 4 square sheets — Correct. The rectangle is 20 cm × 8 cm. It can be divided into four 5 cm × 5 cm squares and four 3 cm × 3 cm squares; total area = 4×25 + 4×9 = 160 cm², matching the sheet’s area.

2. Possible to cut into 10 triangular sheets of equal area — Correct. Total area is 20×8 = 160 cm², so each triangle must have area 16 cm². Divide the sheet into 5 equal vertical strips of width 4 cm; each 4×8 strip can be cut along a diagonal into 2 triangles, each of area 16 cm², giving 10 equal-area triangles.

Hence, both statements are correct.

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