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?
Answer & explanation
Answer: (a) 400 sq m
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). ·