SOLUTION: A farmer needs to enclose three sides of a rectangular pasture with a fence (the fourth side is a river). The farmer has 46 feet of fence and wants the pasture to have an area

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Question 1161216: A farmer needs to enclose three sides of a rectangular pasture with
a fence (the fourth side is a river). The farmer has 46 feet of fence
and wants the pasture to have an area of 260 sq-feet. What should the dimensions of the pasture be? (For the purpose of this problem, the width
will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as
long as possible.)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the smaller side be W and longer side L
if the farmer has 46+feet of fence and needs to enclose three sides of a rectangular pasture, then we have
2W%2BL=46 ......solve for L
L=46-2W.......eq.1

if he wants the pasture to have an area of 260 sq-feet, then
L%2AW=260..........eq.2.......substitute L from eq.1
%2846-2W%29%2AW=260
46W-2W%5E2=260
0=2W%5E2-46W%2B260
2%28W%5E2-23W%2B130%29..........factor
2%28W%5E2-10W-13W%2B130%29
2%28%28W%5E2-10W%29-%2813W-130%29%29
2%28W%28W-10%29-13%28W-10%29%29
2%28W+-+10%29+%28W+-+13%29=0
solutions:
if %28W+-+10%29+=0->W+=+10
if %28W+-+13%29+=0->W+=+13
since he wants the length should be as long as possible, the width will be highlight%28W+=+10ft%29
go to
L=46-2W.......eq.1, substitute W
L=46-2%2A10
L=46-20
highlight%28L=26ft%29