Question

Louis want to carpet the rectangular floor of his basement.

The basement has an area of $864$ square feet.

The width of the basement is $\frac{2}{3}$ its length.

What is the length of Louis's basement $?$

Answer 1

Area of rectangle:

Let the length of the rectangular basement be $x$.

Then, the width of the basement will be:

$=$ $\frac{2x}{3}$

Recall the area of rectangle:

$\text{Area of rectangle=length}\times \text{width}$

So, the area of the rectangular basement will be as follows:

$$\begin{gathered} =x\times \left(\frac{2x}{3}\right) \\ =\frac{2x^2}{3} \end{gathered}$$

Since the area of the rectangular basement is $864$ square feet, we get:

$\frac{2x^2}{3}=864$

$\Rightarrow$ $x^2=1296$

$\therefore$ $x=36$

Hence, the length of Louis's basement is $36\text{feet.}$