Question 1161216
 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+L=46}}} ......solve for {{{L}}}

{{{L=46-2W}}}.......eq.1


if he wants the pasture to have an area of {{{260}}} sq-feet, then

{{{L*W=260}}}..........eq.2.......substitute {{{L}}} from eq.1

{{{(46-2W)*W=260}}}

{{{46W-2W^2=260}}}

{{{0=2W^2-46W+260}}}

{{{2(W^2-23W+130)}}}..........factor

{{{2(W^2-10W-13W+130)}}}

{{{2((W^2-10W)-(13W-130))}}}

{{{2(W(W-10)-13(W-10))}}}

{{{2(W - 10) (W - 13)=0}}}

solutions:

if {{{(W - 10) =0}}}->{{{W = 10}}}

if {{{(W - 13) =0}}}->{{{W = 13}}}

since he wants the length should be as long as possible, the width will be {{{highlight(W = 10ft)}}}

go to

{{{L=46-2W}}}.......eq.1, substitute {{{W}}}

{{{L=46-2*10}}}

{{{L=46-20}}}

{{{highlight(L=26ft)}}}