A rectangular garden has a perimeter of 40 m. What is the largest possible area?
Answer and explanation
Correct answer: B. 100 m2
- Step 1: If one side is x, the other is 20 - x, so area A = x(20 - x). Step 2. dA/dx = 20 - 2x = 0 gives x = 10, a square of side 10 m. Step 3. A = 10 x 10 = 100 m2. Answer: 100 m2. Why not the others: 96 m2: That is the area of a 12 m by 8 m garden, which is not the largest. 64 m2: That is the area of a 16 m by 4 m garden. 120 m2: That is more than even the square of side 10 m gives, so it is impossible for this perimeter.
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