5 से॰ मी॰ विकर्ण के आयत में फिट करने के लिए बारह समान वर्गों को रखा गया है। आयत में तीन पंक्तियाँ हैं, प्रत्येक में चार वर्ग हैं। निकटवर्ती वर्गों के बीच कोई रिक्त स्थान नहीं है। प्रत्येक वर्ग का क्षेत्रफल क्या है?
Read this question in English
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 · (d) 25/12 sq cm
उत्तर और व्याख्या · explanation in English
Answer: (c) 1 वर्ग से॰ मी॰
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). ·