Question 862707
A rectangle has an area A, and the length L is k longer than the width w.  What is L, or find a formula for L.  


Unknown variables are w and L.


{{{wL=A}}} and {{{L=w+k}}}; using this formula for L, {{{w=L-k}}}.
Returning to the area relationship,
{{{w*L=A}}}
{{{(L-k)L=A}}}
{{{highlight_green(L^2-kL-A=0)}}}
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The numbers {{{A>0}}} and {{{k>0}}}, so the usage of signs for the solution for L are unmistakable.  Use the solution for the general solution to a quadratic equation with the positive square root form.
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{{{L=(k+sqrt(k^2-4*(-A)))/2}}}
{{{highlight(L=(k+sqrt(k^2+4A))/2)}}}


You can make the substitutions of k=7 and A=198 and compute L.