A farmer with 570 ft of fencing wants to enclose a rectangular area and then divide it into 4 pens...

Question

A farmer with 570 ft of fencing wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? (a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area, A? If so, estimate it. (Round your answer to the nearest thousand.) (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. O Let x denote the length of the perimeter. Let y denote the length of the dividers. O Let x denote the length of the dividers. Let y denote the length of the perimeter O Let y denote the length of each of two sides and three dividers. Let x denote the length of the other two sides. O Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides (c) Write an expression for the total area. A= ft2 (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the total area as a function of x A= ft2

Komalavalli · Accepted Answer

a) Given perimeter = 570 ft
Dividing the area into 4 pens gives us 5 parallel sides 
Width of the rectangle is 2y
Length of a parallel side p = 570 -2y/5
Lets us assume 4 possible length of parallel sides 
(70,200),(30,300),(110,100),(75,

A farmer with 570 ft of fencing wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the...

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