A basement has 864 square feet. The width of the basement is 2/3 its length. What is the length of the basement?
see below
http://www.jiskha.com/display.cgi?id=1455913440
24 feet
To find the length of the basement, we need to set up and solve an equation based on the given information.
Let's denote the length of the basement as "L". According to the given information, the width of the basement is 2/3 its length.
Width = 2/3 * Length
We also know that the area of the basement is 864 square feet. The formula for calculating the area of a rectangle is:
Area = Length * Width
Substituting the expressions for length and width into the area formula, we have:
864 = L * (2/3 * L)
To simplify the equation, we can multiply both sides by 3 to eliminate the fraction:
3 * 864 = L * 2 * L
2592 = 2 * L^2
Next, divide both sides of the equation by 2 to isolate L^2:
L^2 = 2592 / 2
L^2 = 1296
Now, we can take the square root of both sides to solve for L:
L = √1296
L = 36
Therefore, the length of the basement is 36 feet.