louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basement is 2/3 its length. What is the length of Louis' s basement?
\(x-\ length\\\\ \frac{2}{3}x-\ width\\\\ Area=\ length*width\\\\ 864=x*\frac{2}{3}x\\\\ 864=\frac{2}{3}x^2\ \ \ | divide\ by\ \frac{2}{3}\\\\ 864*\frac{3}{2}=x^2\\\\ 432*3=x^2\\\\ 1296=x^2\ \ \ | \sqrt{}\\\\ x=36ft\\\\ Length\ is \ equal\ to\ 36ft.\)
By definition, the area of a rectangle is given by:
\(A = w * l
\)
Where,
w: width of the rectangle
l: length of the rectangle
Substituting values in the given equation we have:
\(864 = (\frac{2}{3} l) * (l)
\)
From here, we clear the value of l.
We have then:
\(l ^ 2 = (\frac{3}{2}) * (864)
l ^ 2 = 1296
\)
\(l = \sqrt{1296}
l = 36
\)
Answer:
the length of Louis' s basement is:
\(l = 36 feet\)