Twelve equal squares are placed to fit in a rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?
Answer & explanation
Answer: (c) 1 sq cm
With squares of side s, the rectangle measures 4s by 3s, so its diagonal is 5s by Pythagoras. 5s = 5 cm gives s = 1 cm and an area of 1 sq cm.
- Let each square have side s; the rectangle is 4s long and 3s wide.
- Diagonal = √((4s)² + (3s)²) = 5s.
- 5s = 5, so s = 1 cm and each square's area is 1 sq cm.
- Check: a 4 cm × 3 cm rectangle has diagonal √25 = 5 cm.
Remember · Spot the 3-4-5 triangle: sides in the ratio 3 : 4 make the diagonal 5 parts.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·