Answer:
The largest area enclosed is A = xy = 6 feet [tex]\times[/tex] 6 feet = 36 [tex]feet^{2}[/tex]
Step-by-step explanation:
i) The perimeter of the area is 2[tex]\times[/tex](x + y) =24 ∴ x + y = 12 ∴ y = 12 - x
ii) The area of rectangle enclosed A = xy ⇒ A = x ( 12 - x) = 12x - [tex]x^{2}[/tex]
iii) differentiating both sides of the equation in ii) we get
[tex]\dfrac{dA}{dx} = 12 - 2x = 0[/tex] ⇒ x = 6 feet
iv) Differentiating both sides of equation in iii) we get [tex]\frac{d^{2}A}{dx^{2} }[/tex] = -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 [tex]\times[/tex] 6 feet = 36 [tex]feet^{2}[/tex]