Question

Farmer Ed has 500 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, find the length and width of the plot that will maximize the area. What is the largest area that can be​ enclosed?

Answer 1

Answer:

Answer:

Width=125

Length= 250

Area= 31,250

Answer 2

The length and width of the plot that will maximize the area are:

•Length 250

•Width 125

•The largest area that can be​ enclosed is 31,250

Area = length x width

A= L w

Perimeter =( 2 ×length) + (2×width)

Perimeter = Length + 2×width  

Perimeter = L + 2w

Perimeter is 500

500 = L + 2w

L = 500 - 2w

Let plug in the formula

Area A(w) = L×w = (500- 2w)×w

 

(500 - 2w)×w = 0

500 - 2w = 0 or w=0

500 = 2w

w = 250   or W=0

Since the two solutions are 0 and 250

Average = (250)/2

Average= 250/2

Average = 125

Hence, the max area is at w=125

Length (L)=500 - 2×125

Length (L)= 500 - 250

Length (L) = 250

The dimensions that maximize the area is

Length (L)=250

Width (w)=125

The max area =250 ×125

The max area=31,250

Inconclusion The length and width of the plot that will maximize the area are:

•Length 250

•Width 125

•The largest area that can be​ enclosed is 31,250

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