Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.
As given in the question,
Perimeter of the rectangular area encloses for fencing = 3200 yards
Let 'x' and 'y' be the length and width of the rectangle.
2( x + y ) = 3200
⇒ x + y = 3200/2
⇒y = 1600 - x
Area of rectangular field 'A' = xy
⇒ A = x ( 1600 - x )
⇒ A = 1600x - x²
Differentiate both the side of the equation we get,
dA/dx = 1600 - 2x
For Maximum Area dA/dx = 0
1600 -2x =0
⇒ 2x = 1600
⇒ x= 800 yards
Now, y = 1600 - 800
= 800 yards
Maximum area = (800) (800)
= 640,000 square yards
Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.
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