SOLUTION: A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensi

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Question 806116: A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensions of the enclosed region.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas.
If the total enclosed area is 225 ft2, find the dimensions of the enclosed region.
:
The fence with 4 widths:
2L + 4W = 86
simplify, divide by 2
L + 2w = 43
L = (43-2W)
:
L*W = 225
Replace L
(43-2w)w = 225
43w - 2w^2 = 225
A quadratic equation
-2w^2 + 43w - 225 = 0
multiply by -1, easier to fator
2w^2 - 43w + 225 = 0
(2w-25)(w-9)
Two solutions here
2w = 25
w = 12.5 ft is the width then L = 43-25 = 18 ft is the length
and
w = 9 ft is the width then L = 43-18 = 25 ft is the length