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Answer:
The largest area enclosed is A = xy = 6 feet 6 feet = 36
Step-by-step explanation:
i) The perimeter of the area is 2(x + y) =24 ∴ x + y = 12 ∴ y = 12 - x
ii) The area of rectangle enclosed A = xy ⇒ A = x ( 12 - x) = 12x -
iii) differentiating both sides of the equation in ii) we get
⇒ x = 6 feet
iv) Differentiating both sides of equation in iii) we get = -2
Therefore the area enclosed is maximum as the double derivative is negative
v) therefore for largest area enclosed x = 6 feet and y = 12 - 6 = 6 feet
vi) therefore the largest area enclosed is
A = xy = 6 feet 6 feet = 36