Question 1153352
<br>
Logically, with the rectangle having an area of 35 square feet, and with the perimeter and area both being whole numbers, the probable dimensions of the rug are 5 feet by 7 feet -- and those dimensions give the correct perimeter of 24 feet.<br>
With formal algebra....<br>
{{{xy = 35}}}
{{{2x+2y=24}}}<br>
Solve the second equation for either variable and substitute in the first equation:<br>
{{{x+y = 12}}}
{{{y = 12-x}}}
{{{x(12-x) = 35}}}
{{{12x-x^2 = 35}}}
{{{x^2-12x+35 = 0}}}
{{{(x-7)(x-5) = 0}}}
{{{x = 7}}} or {{{x = 5}}}<br>
The dimensions of the rug are x=7 and (12-x) = 5.<br>