Rachel wants to carpet the rectangular 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 Rachel's basement.
To find the length of Rachel's basement, we first need to set up an equation based on the given information.
Let's assume the length of the basement as "L". According to the problem, the width of the basement is 2/3 of its length, so the width would be (2/3) * L.
The area of the rectangle can be calculated using the formula: Area = Length * Width. From the problem, we know that the area of the basement is 864 square feet. So, we can form the equation:
864 = L * (2/3) * L
To solve this equation, we need to simplify it. Multiplying L with (2/3) can be done by multiplying the numerators (2) and (L) and the denominators (3) and (1):
864 = (2/3) * L^2
Next, we can isolate L^2 by dividing both sides of the equation by (2/3):
(864) / (2/3) = L^2
Now, simplify the right side of the equation by multiplying the numerator (864) by the reciprocal of (2/3), which is (3/2):
(864) * (3/2) = L^2
2592/2 = L^2
1296 = L^2
To find the length of the basement, we can take the square root of both sides of the equation:
√1296 = √L^2
36 = L
Therefore, the length of Rachel's basement is 36 feet.
W = 2/3L
WL = 864
Substitute 2/3L for W in the second equation and solve for L. Insert that value into the first equation to solve for W. Check by putting both values into the second equation.