Answer: 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
