Question 877931
The area of a rectangle is A square meters , and the length of the rectangle is k more than m times the width. Find the dimensions of the rectangle.


Let w = width 
Let L = length
Later, let k=1 and m=2.


Description gives {{{L=mw+k}}}, and {{{wL=A}}}.
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{{{w(mw+k)=A}}}
{{{mw^2+kw=A}}}
{{{mw^2+kw-A=0}}}
You could do the numberic variable substitutions now in anticipation that the quadratic is factorable.  Solve for w and use the result or the value to find L.

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{{{2w^2+w-66=0}}}
Try for factorability,
{{{(2w-11)(w+6)=0}}}
Use the solution {{{2w-11=0}}}
{{{2w=11}}}
{{{highlight(w=11/2)}}}.
{{{highlight(L=12)}}}.