Question 25853: A rancher with 800 feet of fencing wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the three pens?
i'm not allowed to use trial and error, only algebra. I've tried like 6 different equations where x=y or x=3y, i just can't figure it out. Please help!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A rancher with 800 feet of fencing wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the three pens?
i'm not allowed to use trial and error, only algebra. I've tried like 6 different equations where x=y or x=3y, i just can't figure it out. Please
LET LENGTH AND WIDTH OF FIELD BE L AND B
FENCING NEEDED AROUND THE FIELD =2L+2B
FENCING FOR THE 3 PENS OR 2 DIVIDERS ALONG LENGTH =2L
TOTAL FENCING =2L+2B+2L=4L+2B=800
OR ....2L+B=400...OR B = 400-2L
AREA = LB = L(400-2L)=2(200L-L^2)=2{100^2-(L-100)^2}
THIS WILL BE MAXIMUM WHEN l+!)) AND MAXIMUM AREA IS
2*100^2=20000 SQ.FT.
|
|
|
