Louis wants to carpet the rectangle 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?

the length of Louis's basement is 36 feet.

Step-by-step explanation:

Let L represent the length of Louis's basement.

Let W represent the width of Louis's basement.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The basement has an area of 864 square feet. It means that

LW = 864 - - - - - - - - 1

The width of the basement is 2/3 its length. This means that

W = 2/3 × L

W = 2L/3

Substituting W = 2L/3 into equation 1, it becomes

L(2L/3) = 864

2L²/3 = 864

Cross multiplying, it becomes

2L² = 864 × 3

2L² = 2592

L² = 2592/2 = 1296

L = √1296

L = 36

W = 2L/3 = (2 × 36)/3

W = 24

step-by-step explanation: