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The back of Monique’s property is a creek. Monique would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 180 feet of fence available, what is the maximum possible area of the corral?

Respuesta :

Answer:

4050 sq. feet.

Step-by-step explanation:

Fencing is done on three sides of the rectangular area.

Given that there are 180 feet of fence available.

Then 2L + W = 180 ........(1), where L = length and W = width, of the rectangular plot.

Now, the area of the plot is given by A = LW

Now, from equation (1), we ger A = L (180 - 2L) ..... (2)

Then differentiating with respect to L in the both sides we get,

[tex]\frac{dA}{dL} = 180 - 4L =0[/tex] {Since condition for Area to be maximum is [tex]\frac{dA}{dL}=0[/tex]}

⇒ L = 45 feet.

Now, from equation (2), we have [tex]A_{max} =L(180-2L) = 45(180 - 90) =4050[/tex] square feet.