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.