Question 935055
L for length, w for width.
A for area.
L and w are unknown.


The length of a rectangle is k yards
less than m times the width w, and the area of the rectangle is A yds^2.
Find the dimensions, w and L.


{{{wL=A}}},    {{{L=mw-k}}}


{{{w(mw-k)=A}}}
{{{mw^2-kw=A}}}
{{{highlight_green(mw^2-kw-A=0)}}}


Beginners would rely on the quadratic expression being factorable when m, k, and A are substituted,
and then solution for w would be found that way (factoring).  Intermediate level and higher students
could solve for w either by quadratic formula solution, or competing the square.


Directly using general solution,
{{{highlight(w=(k+- sqrt(k^2-4*m*A))/(2m))}}}
One of those will make sense but not the other.  Substitute the values for k, m, and A, evaluate w,
and then use the value to evaluate L.