Question 632566: I decide to take up alpaca farming. I will build an alpaca pan to my house. (since it is next to my house, i don't need any fencing on the side where my house is. My house is huge so I don't have to worry about that side being too short.) I have 800 feet of fencing. I am going to make a rectangular fence.
A. If I want the pen to have an area of 15,200 sq feet, what should the dimensions be?
B. If i want the pen to have an area of 100,000 sq feet, what should the dimensions be?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I will build an alpaca pen next to my house.
(since it is next to my house, i don't need any fencing on the side where my house is.
My house is huge so I don't have to worry about that side being too short.)
I have 800 feet of fencing. I am going to make a rectangular fence.
:
A. If I want the pen to have an area of 15,200 sq feet, what should the dimensions be?
Let L = the length of the pen
Let W = the width
one length is the house, the length of the fence required will be:
L + 2W = 800
L = (800-2W)
The area: L * W = 15200
Replace L with (800-2W)
W(800-2W) = 15200
-2W^2 + 800W = 15200
A quadratic equation
0 = 2W^2 - 800W + 15200
You can use the quadratic formula here but this will factor to
(2W - 40)(W - 380) = 0
Two solutions
2W = 40
W = 20
Use this as the width, then
800-2(20) = 760 is the length
(If that is longer than your house, you can use 380 as the width then
800-2(380) = 40 is the length)
:
B. If i want the pen to have an area of 100,000 sq feet, what should the dimensions be?
With 800 ft of fencing it is not possible to enclose 100000 sq/ft
Max area is 80000 sq/ft with a dimension of a 400 by 200 ft pen
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