Question 273838
If {{{x}}} and {{{y}}} are the lengths of the sides in inches, and
{{{p}}} = perimeter
The formula is:
{{{p = 2x + 2y}}} 
given:
{{{p = 52}}} in
{{{2x + 2y = 52}}}
subtract {{{2x}}} from both sides
{{{2y = -2x + 52}}}
divide both sides by {{{2}}}
{{{y = -x + 26}}}
I'll plot this line
{{{ graph( 500, 500, -5, 30, -5, 30, -x + 26) }}}
Any point (x,y) on this line is a solution to {{{2x + 2y = 52}}}
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I can find 3 whole-number solutions by trying different {{{x}}}'s
and finding the {{{y}}}'s
I'll try {{{x = 8}}}
{{{y = -8 + 26}}}
{{{y = 18}}}
so, (8,18) is a solution
I'll try {{{x = 16}}}
{{{y = -16 + 26}}}
{{{y = 10}}}
so, (16,10) is a solution
I'll try {{{x = 13}}}
{{{y = -13 + 26}}}
{{{y = 13}}}
so, (13,13) is a solution
Notice that you can't make either {{{x}}} or {{{y}}} zero,
since you wouldn't have a rectangle anymore, just
a straight line