एक खेत आयताकार आकृति में है जिसकी लम्बाई X₁ मीटर और चौड़ाई X₂ मीटर है .(X₁ और X₂ चर हैं)। यदि X₁ + X₂ = 40 मीटर है तो उस खेत का क्षेत्रफल निम्नलिखित किस एक मान से अधिक नहीं होगा ?
Read this question in English
An agricultural field is in the form of a rectangle having length X₁ meters and breadth X₂ meters (X₁ and X₂ are variable). If X₁ + X₂ = 40 meters, then the area of the agricultural field will not exceed which one of the following values?
(a) 400 sq m · (b) 300 sq m · (c) 200 sq m · (d) 80 sq m
उत्तर और व्याख्या · explanation in English
Answer: (a) 400 वर्ग मीटर
When the length and breadth add up to 40 m, the area is greatest when the rectangle is a square of side 20 m. So the area can never exceed 20 × 20 = 400 sq m.
- For a fixed sum X₁ + X₂ = 40, the product X₁ × X₂ is largest when X₁ = X₂ = 20.
- Maximum area = 20 × 20 = 400 sq m.
- Check: 19 × 21 = 399 and 10 × 30 = 300, both below 400.
Remember · For a fixed sum, a product is largest when the parts are equal.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·