Answer :
[tex]x-\ length\\\\
\frac{2}{3}x-\ width\\\\
Area=\ length*width\\\\
864=x*\frac{2}{3}x\\\\
864=\frac{2}{3}x^2\ \ \ | divide\ by\ \frac{2}{3}\\\\
864*\frac{3}{2}=x^2\\\\
432*3=x^2\\\\
1296=x^2\ \ \ | \sqrt{}\\\\
x=36ft\\\\
Length\ is \ equal\ to\ 36ft.[/tex]
By definition, the area of a rectangle is given by:
[tex] A = w * l
[/tex]
Where,
w: width of the rectangle
l: length of the rectangle
Substituting values in the given equation we have:
[tex] 864 = (\frac{2}{3} l) * (l)
[/tex]
From here, we clear the value of l.
We have then:
[tex] l ^ 2 = (\frac{3}{2}) * (864)
l ^ 2 = 1296
[/tex]
[tex] l = \sqrt{1296}
l = 36
[/tex]
Answer:
the length of Louis' s basement is:
[tex] l = 36 feet [/tex]
