Final answer:
The width of the rectangle is 7 feet and the length is 16 feet. A quadratic equation is derived from the given area and the relationship between the length and width, and solved to find the dimensions.
Step-by-step explanation:
Let the width of the rectangle be w feet. According to the problem, the length is 2ft more than twice the width, so the length is 2w + 2. The area of the rectangle is given by the product of its length and width, which we know is 122ft2. Therefore, we can construct the equation w(2w + 2) = 122.
Expanding this, we have 2w2 + 2w = 122 and moving all terms to one side, 2w2 + 2w - 122 = 0. This is a quadratic equation, which we can solve by factoring, completing the square, or using the quadratic formula. After solving, we find that w = 7 and therefore, the length l is 2(7) + 2 = 16 feet.
So, the dimensions of the rectangle are 7 feet by 16 feet.