Final answer:
The width of the rectangular rug is 15 feet and the length is 17 feet.
Step-by-step explanation:
To find the dimensions of the rectangular rug, let's set up an equation using the given information. Let's say the width of the rug is 'x' feet. According to the problem, the length of the rug is 2 feet longer than the width, so the length would be 'x+2' feet.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 64 feet, so we can set up the equation:
2(x + x + 2) = 64 [Perimeter formula: P = 2(L + W)]
4x + 4 = 64 [Combine like terms]
4x = 60 [Subtract 4 from both sides]
x = 15 [Divide both sides by 4]
Therefore, the width of the rug is 15 feet and the length is (15 + 2) = 17 feet.