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?
- (a) 5/7 sq cm
- (b) 7/5 sq cm
- (c) 1 sq cm ✓ UPSC's answer
- (d) 25/12 sq cm
Why the answer is (c)
• Let each square have side s cm. Three rows of four squares make a rectangle 4s long and 3s wide.
• Its diagonal is 5 cm, so (4s)² + (3s)² = 5², that is 16s² + 9s² = 25, giving 25s² = 25.
• So s² = 1: each square has an area of 1 sq cm, option (c).
Why the other options are wrong
- (a) 5/7 sq cm
- 5/7 sq cm does not satisfy 25s² = 25.
- (b) 7/5 sq cm
- 7/5 sq cm does not satisfy 25s² = 25.
- (d) 25/12 sq cm
- 25/12 sq cm divides the diagonal squared by 12, but the diagonal squared equals 25s², not 12s².
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.