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?
Answer & explanation
Answer: (c) Both 1 and 2
Two 8 cm squares plus two 4 cm squares use up the whole 20 × 8 sheet, and five 4 × 8 strips cut along their diagonals give 10 equal triangles. Both statements are possible.
- Statement 1: cut two 8 × 8 squares from the 20 × 8 sheet, leaving a 4 × 8 strip; cut that into two 4 × 4 squares. That is exactly 4 square sheets with nothing left over.
- Statement 2: cut the sheet into five 4 × 8 rectangles and cut each along a diagonal: 10 triangles, each of area 16 cm² (160 ÷ 10).
- Both statements are correct.
- ✓ 1. 8 × 8 + 8 × 8 + 4 × 4 + 4 × 4 = 64 + 64 + 16 + 16 = 160 cm², the whole sheet.
- ✓ 2. Five 4 × 8 rectangles halved diagonally give 10 triangles of 16 cm² each.
Remember · ‘It is possible’ needs only one construction; the squares need not be equal unless the item says so.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·