Devon is planning to build exercise pens for his three horses. Because of the space that he has available, he has decided to create three rectangular pens as shown in the diagram.

Question

Devon is planning to build exercise pens for his three horses.  Because of the space that he has available, he has decided to create three rectangular pens as shown in the diagram. Each of the three rectangular pens has the same size and shape. He has been advised that the perimeter of each of the small pens should be 440 feet. He decides to use 1200 feet of fencing, because that is all he can afford.

Diagram is like this: first rectangular pen has  W on the left and L on top, and is also more  wider than length. 2nd rectangular pen is the exact same as the first one and is connected to it on its left side. The first rectangular pen is connected to the 2nd pen on its right side. And lastly the last one has W on top and L on the right and is more longer than wider. And it’s connected to the 2nd pen in its left side. The 2nd pen is connected to the 3rd pen on its right side. 

a. write a system of equations that models this situation.

b. What dimensions should Devin have for each pen? Make sure to show how you solved the system algebraically.

c. What would the equations be if the total amount of fencing Devon could afford was 800 feet? (Write a new system reflecting this change)

d. Solve this new system algebraically and explain the solution. Make sure to show how you solved the system.

Answer 1

If W=L

then all 3 pens are the same area LxW, with total area 3LW

Then 5L+5W = 440

10W = 440

W = 44 = L

each pen is 44 by 44 feet

If you really want W>L and L>W,

you have a contradiction, but closest you can come to that is make W=L

or maybe W=44+ epsilon and L= 44 ft + epsilon where epsilon is a an infinitely small surreal number. and W similarly =44 ft + epsilon

800 perimeter makes L=W = 80 feet with each pen 80 by 80 feet

odds are the problem probably: read width is greater than or equal to length and the last pen had length is greater than or equal to width

W>L and L>W, which is not a contradiction but a way of saying W=L