Question 845367
x and y are the dimensions, one of them length and the other width.


Area description means xy=56 and perimeter description means 2x+2y=30.  For just solving the problem asked, solving for x and y is more important and would be done first.


The perimeter equation is easily simplified to x+y=15.  This also directly gives y=15-x and can be substituted....

{{{xy=56}}}
{{{x(15-x)=56}}}
{{{15x-x^2=56}}}
{{{15x-56-x^2=0}}}
{{{x^2-15x+56=0}}}
{{{highlight(highlight((x-8)(x-7)=0))}}}
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Easily mentally skipping steps, the difference between the length and width is ONE UNIT.
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In case one could not skip the steps, then continuing form the factored quadratic equation, either x=7 or x=8.
Using area equation xy=56, find that y=56/x.
That means either y=56/7=8  or  y=56/8=7.
Either way, the difference between x and y is 1.