Respuesta :
Given:
Given that Louis wants to carpet the rectangular floor of his basement.
The basement has an area of 2000 square feet. The width of the basement is [tex]\frac{4}{5}[/tex] its length.
We need to determine the length of the Louis's basement.
Length of Louis's basement:
Let l denote the length of the basement.
Let w denote the width of the basement.
Since, width is [tex]\frac{4}{5}[/tex] its length, it can be written as [tex]w=\frac{4}{5}l[/tex]
Substituting these values in the area of the rectangle formula, we get;
[tex]A=lw[/tex]
[tex]2000=l(\frac{4}{5}l)[/tex]
[tex]2000=\frac{4}{5}l^2[/tex]
Multiplying both sides by [tex]\frac{5}{4}[/tex], we get;
[tex]\frac{10000}{4}=l^2[/tex]
[tex]2500=l^2[/tex]
Taking square root on both sides, we have;
[tex]50=l[/tex]
Thus, the length of Louis's basement is 50 feet.
