Answer:
The length of Louise’s basement is <u>90 feet</u>.
Step-by-step explanation:
Given:
Louis wants to carpet the rectangular floor of his basement.
The basement has an area of 4860 square feet.
The width of the basement is 3/5 it’s length.
Now, to find the length of Louise’s basement.
Let the length of basement be ![x.](https://tex.z-dn.net/?f=x.)
So, the width is:
![\frac{3}{5}\ of\ x\\=\frac{3}{5}\times x\\=\frac{3x}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%5C%20of%5C%20x%5C%5C%3D%5Cfrac%7B3%7D%7B5%7D%5Ctimes%20x%5C%5C%3D%5Cfrac%7B3x%7D%7B5%7D)
Area of the basement = 4860 square feet.
Now, to get the width of basement we put formula:
![Area=length\times width](https://tex.z-dn.net/?f=Area%3Dlength%5Ctimes%20width)
![4860=x\times \frac{3x}{5}](https://tex.z-dn.net/?f=4860%3Dx%5Ctimes%20%5Cfrac%7B3x%7D%7B5%7D)
![4860=\frac{3x^2}{5}](https://tex.z-dn.net/?f=4860%3D%5Cfrac%7B3x%5E2%7D%7B5%7D)
<em>Multiplying both sides by 5 we get:</em>
![24300=3x^2](https://tex.z-dn.net/?f=24300%3D3x%5E2)
<em>Dividing both sides by 3 we get:</em>
![8100=x^2](https://tex.z-dn.net/?f=8100%3Dx%5E2)
<em>Using square root on both sides we get:</em>
![90=x](https://tex.z-dn.net/?f=90%3Dx)
![x=90\ feet.](https://tex.z-dn.net/?f=x%3D90%5C%20feet.)
Therefore, the length of Louise’s basement is 90 feet.