Final answer:
The dimensions of the rug with an area of 6 square feet and whose length is 4 feet more than twice its width are 1.5 feet by 7 feet.
Step-by-step explanation:
To find the dimensions of a rectangular rug with an area of 6 square feet where the length is 4 feet more than twice its width, we need to set up an equation using the area formula for rectangles, which is Area = length × width.
Let the width of the rug be w feet. According to the problem, the length (l) will then be 2w + 4 feet.
Now, set up the equation: 6 = w × (2w + 4). To solve for w, we'll distribute the width into the parenthesis and obtain a quadratic equation:
6 = 2w^2 + 4w.
Subtract 6 from both sides to set the equation to zero:
0 = 2w^2 + 4w - 6.
We'll solve this quadratic equation by factoring, completing the square or using the quadratic formula. The determination of the correct width allows us to then find the length by substituting back into l = 2w + 4.
After solving the equation, we find that the width w of the rug is 1.5 feet and the length l is 7 feet. Therefore, the dimensions of the rug are 1.5 feet by 7 feet.