The area of a rectangular carpet is
12 square feet. The length is four feet more than the width. Find the length and the width of the carpet.
w (w + 4) = 12
w^2 + 4w - 12 = 0
(w + 6)(w - 2) = 0
let x=the width
then x+4 = the length
x+4+x=12
To find the length and width of the carpet, we can set up a system of equations based on the given information.
Let's represent the width of the carpet as "w" (in feet). Since the length is four feet more than the width, we can express the length as "w + 4" (in feet).
The area of a rectangle is calculated by multiplying the length by the width. In this case, we know that the area is 12 square feet. So we have the equation:
Length × Width = Area
(w + 4) × w = 12
Expanding the equation, we get:
w² + 4w = 12
Rearranging this equation into standard quadratic form, we get:
w² + 4w - 12 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or quadratic formula.
Factoring the equation w² + 4w - 12 = 0, we get:
(w + 6)(w - 2) = 0
Setting each factor equal to zero, we find two possible solutions: w = -6 or w = 2.
Since the width of a rectangle cannot be negative, we discard the extraneous solution w = -6.
Therefore, the width of the carpet is w = 2 feet. To find the length, we can substitute this value back into the equation we previously established:
Length = Width + 4
Length = 2 + 4
Length = 6 feet
So, the length of the carpet is 6 feet, and the width of the carpet is 2 feet.