Question 46952
l = length (in feet)
w = width (in feet)

We have that, by "The length of a rectangle is 2feet less than 3times its width":

{{{l = 3w - 2}}}

And we have that (since the area of a rectangle is calculated by multiplying length and width): 

{{{wl = 21}}}

Substituting l:

{{{w(3w - 2) = 21}}}
{{{3w^2 - 2w = 21}}}
{{{3w^2 - 2w - 21 = 0}}}

*[invoke quadratic "w", 3, -2, -21 ]

Since we only want positive solutions, w = 3, and we can say that (based on the first statement):

{{{l = 3*3 - 2}}}
{{{l = 7}}}

Verifying, we get that {{{7*3 = 21}}}.