Question 862076
w for width
L for length
k = how much is length than the width; {{{k>0}}}.
m = a factor applied to the width as part of description.  Usually this is a natural number.
A = area of rectangegle
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The only unknown variables are L and w.
You are given that k=1, m=4, A=39.


{{{L=-k+m*w}}}, the first sentence in the description.
{{{wL=A}}}, the second sentence in description.
{{{w(-k+mw)=A}}}
{{{w(mw-k)=A}}}
{{{mw^2-kw=A}}}
{{{mw^2-kw-A=0}}}
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Values given may often be chosen to make the resulting quadratic equation to be factorable.  This will make the solution for w easily found.  In "Introductory Algebra", you can usually depend on this factorability; after that, you cannot always depend on this factorability and will need to use general solution of a quadratic equation.  Is this example factorable?


If not, or even if it is, 
{{{w=(k+sqrt(1-4*m(-A)))/(2m)}}}
{{{highlight(w=(k+sqrt(1+4mA))/(2m))}}}, choosing the form with the positive square root, because we know w must be positive.