Question 826832
x length
w width
Perimeter, {{{2x+2w=28}}}, simplifies to {{{x+w=14}}}.


{{{x-w>=4}}}.


Solve for either variable from the equation and substitute it into the inequality.
{{{w=14-x}}};
{{{x-(14-x)>=4}}}
{{{x-14+x>=4}}}
{{{2x-14>=4}}}
{{{x-7>=2}}}
{{{highlight(x>=9)}}}
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Note that {{{x<14}}} because of perimeter restriction.  This means, {{{highlight(9<=x<14)}}}.   You can determine the corresponding sizes for w.
w=14-x, so 14-9=5.  This would mean, {{{highlight(5>=w>0)}}}.
Those intervals for x and w allow an infinite set of pairs.
One example is 9 by 5.  Another example is 13 by 1.