Question

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?

Answer 1

$x-\ length\\\\ \frac{2}{3}x-\ width\\\\ Area=\ length*width\\\\ 864=x*\frac{2}{3}x\\\\ 864=\frac{2}{3}x^2\ \ \ | divide\ by\ \frac{2}{3}\\\\ 864*\frac{3}{2}=x^2\\\\ 432*3=x^2\\\\ 1296=x^2\ \ \ | \sqrt{}\\\\ x=36ft\\\\ Length\ is \ equal\ to\ 36ft.$

Answer 2

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:

$l = 36 feet$