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

(a) 1 only
(b) 2 only
(c) Both 1 and 2 ✓ UPSC's answer
(d) Neither 1 nor 2

Why the answer is (c)

• Area of the rectangular sheet = 20 cm × 8 cm = 160 cm².

• For statement 1, cut the 20 cm length into 8 cm + 8 cm + 4 cm, giving two 8 cm × 8 cm squares and one 4 cm × 8 cm rectangle.

• Cut the 4 cm × 8 cm rectangle into two 4 cm × 4 cm squares, giving exactly 4 square sheets.

• For statement 2, divide the 20 cm length into 5 equal parts of 4 cm, making five 4 cm × 8 cm rectangles of area 32 cm² each.

• Cut each 4 cm × 8 cm rectangle along one diagonal into two triangles, giving 10 triangles of area 16 cm² each, equal to 160 cm² ÷ 10.

• Therefore both statements are correct, so option (c) follows.

Why the other options are wrong

(a) 1 only: Option (a) is wrong because statement 2 is correct, as the sheet can be divided into five 4 cm × 8 cm rectangles and each cut diagonally into two 16 cm² triangles.
(b) 2 only: Option (b) is wrong because statement 1 is correct, as the 20 cm × 8 cm sheet can be cut into two 8 cm × 8 cm squares and two 4 cm × 4 cm squares.
(d) Neither 1 nor 2: Option (d) is wrong because both statements are correct, not neither.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.