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प्रश्न
A garden is to be laid out in a rectangular area and protected by a wire fence. What is the largest possible area of the fenced garden with 40 meters of wire?
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उत्तर
Perimeter = 40 m
2(l + b) = 40
⇒ l + b = 20
Let l = x m
b = (20 – x)m
Area = l × b
= x(20 – x)
= 20x – x2
To find the maximum area
A(x) = 20x – x2
A'(x) = 20 – 2x
A”(x) = – 2
A'(x) = 0
⇒ 20 – 2x = 0
⇒ x = 10
x = 10 is a maximum point
∴ Maximum Area = x(20 – x)
= 10(20 – 10)
= 10 × 10
= 100 sq.m.
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