Question 1075201: A farmer has 160 yd of fencing material and wants to enclose three rectangular pens. The farmer wants each pen to be 250 square yd. What will be the dimensions of each pen?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A farmer has 160 yd of fencing material and wants to enclose three rectangular pens.
The farmer wants each pen to be 250 square yd.
What will be the dimensions of each pen?
:
Let w = the width, each side and the two which divide it into 3 ea 250 sq/yd fields
let L = the Length
Then
2L + 4w = 160
Simpify, divide by 2
L + 2w = 160
L = -2w + 160
Total area = 3(250) = 750 sq/yd
L * w = 750
replace L with (-2w+160)
w(-2w+160) = 750
-2w^2 + 160w - 750 = 0
simplify, divide by -2
w^2 = 80w + 375 = 0
Factors to
(w - 75)(w - 5) = 0
Two solutions
w = 75 yds
w = 5 yds, use this for width, (the other solution will work too)
find the length
L = -2(5) + 160
L = -10 + 160
L = 150 yds is the length
:
Confirm that we have 3 fields with 250 sq/yds, divide the length by 3
50 * 5 = 250 sq/yds
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