A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them a much room as possible to run. What are the dimensions of the rectangular pen with the largest area?
Write an expression of the terms of a single variable that would represent the area of a rectangular family.
Find the dimensions of the rectangle with maximum area.
What is another name for this kind of rectangle?

Question

A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them a much room as possible to run. What are the dimensions of the rectangular pen with the largest area? 
Write an expression of the terms of a single variable that would represent the area of a rectangular family.
Find the dimensions of the rectangle with maximum area.
What is another name for this kind of rectangle?

anonymous · Answer

Perimeter of pen must be 120. P =2w+2L So you can figure that the pen will be 30 on each side. You can then do a guess and check to get other combinations. 20 by 40, 10 by 50.  You also know Area is A =w*l. So plug in your different choices. 30*30=900
20*40=800  10*50=500 to figure out largest area possible.

anonymous · Answer

We are given the constraint: (the perimeter of the rectangle)
120 = 2L + 2w
Simplified to: 
60 = L + w
We want to maximize area under this constraint. Area of a rectangle is given by:
A = L*w
Solve for L in the perimeter equation
L = 60-w

A = (60-w)*w
A = 60w-w^2
This is a quadratic function of area, the variable which you want to maximize. To find the maximum point, simply take the derivative of this function and set it equal to zero (the top part of the parabola)
A'= 60-2w = 0
-2w = -60
w = 30
therefore L = 30

This object is a square with side length of 30.

anonymous · Answer

what is the diagram for this problem?

anonymous · Answer

@cutiecomittee123 @wesbrett @dagrothus

ohmybookness · Answer

did you end up finding the diagram?