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Julli [10]
3 years ago
7

louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basem

ent is 2/3 its length. What is the length of Louis' s basement?
Mathematics
2 answers:
ivolga24 [154]3 years ago
8 0
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.
evablogger [386]3 years ago
5 0

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

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