A man wants to build a rectangular enclosure with one side bounded by a straight river. If he has 200 m of fencing material, the maximum area he can enclose is:
A man wants to build a rectangular enclosure with one side bounded by a straight river. If he has 200 m of fencing material, the maximum area he can enclose is:
- A. 2500 m²
- B. 10000 m²
- C. 5000 m²
- D. 7500 m²
Answer: C) 5000 m²
Explanation: Let river side have length x, and two adjacent sides be y. x + 2y = 200. Area A = x y = (200 - 2y)y = 200y - 2y². A' = 200 - 4y = 0 → y = 50. x = 100. Max Area = 100 × 50 = 5000 m².
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