The length of a rectangular carpet is 6 feet greater than twice its width. If the area is 72 square feet, find the carpet's length and width.
w(2w+6) = 72
2w^2 + 6w - 72 = 0
w^2 + 3w - 36 = 0
w = 3/2 (√17 - 1)
Odd answer. These usually involve integers. Typo?
To solve this problem, we need to use the given information and set up equations based on the given conditions.
Let's assume that the width of the rectangular carpet is "w" feet.
According to the problem, the length of the carpet is 6 feet greater than twice its width. So, the length can be expressed as (2w + 6) feet.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 72 square feet.
So, we set up an equation:
Area = Length * Width
72 = (2w + 6) * w
Now, we can solve this equation to find the value of "w" and then calculate the length.
Expanding the equation:
72 = 2w^2 + 6w
Rearranging the equation to set it equal to zero:
2w^2 + 6w - 72 = 0
Next, we can factor or use the quadratic formula to solve for "w". Let's use factorization:
2w^2 + 6w - 72 = 0
2(w^2 + 3w - 36) = 0
2(w + 9)(w - 4) = 0
Setting each factor equal to zero and solving for "w":
w + 9 = 0 or w - 4 = 0
If we solve each equation, we get two possible values for "w":
w = -9 or w = 4
However, since the width cannot be negative, we discard w = -9 as an extraneous solution.
Thus, the width of the carpet is w = 4 feet.
To find the length, we can substitute the value of width (w = 4) in the expression we obtained earlier for the length:
Length = 2w + 6
Length = 2(4) + 6
Length = 8 + 6
Length = 14 feet
Therefore, the carpet's width is 4 feet and its length is 14 feet.