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.
Thank you very much, it helped me a lot. :)
To find the length of Rachel's basement, we need to set up an equation using the information given. Let's assume the length of the basement is "L" feet.
According to the given information, the width of the basement is 2/3 its length. So, the width would be (2/3) * L = (2L/3) feet.
The area of a rectangle is given by the formula: Area = length * width.
We are told that the area of Rachel's basement is 864 square feet. So, the equation becomes: 864 = L * (2L/3).
To solve this equation, we can multiply both sides by 3 to get rid of the fraction: 3 * 864 = L * (2L).
Simplifying further, we get: 2592 = 2L^2.
Divide both sides by 2: 2592/2 = L^2.
Simplifying, we have: 1296 = L^2.
To find the value of L, we take the square root of both sides: √1296 = √(L^2).
Simplifying further, we get: 36 = L.
Therefore, the length of Rachel's basement is 36 feet.
This problem looks similar to the other math problem posted here. OwO
Anyway, first represent the unknowns.
Let x = length
since the width is 2/3 of the length,
Let (2/3)x = width
Recall that the area of rectangle is just width multiplied by the length,
A = w * l
Substituting,
864 = (2/3)x * x
864 = (2/3)x^2
864 * 3/2 = x^2
1296 = x^2
Get the square root of both sides,
x = 36 feet (length)
Note that you should only get the positive root since dimensions (length, width, etc.) cannot be negative.
Hope this helps~ `u`