Final answer:
To find the length and width of the rug, we need to use the Pythagorean theorem and set up an equation based on the given information. Solving this equation will give us the dimensions of the rug.
Step-by-step explanation:
To find the length and width of the rug, we can use the information given in the problem. Let's assign the width of the rug as 'w'. Since the length is 4 feet more than twice the width, we can express the length as (2w + 4). Now, we can use the Pythagorean theorem to find the width and length of the rug.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since the diagonal of the rug is the hypotenuse of the rectangle, we have the equation: (width)^2 + (length)^2 = (diagonal)^2.
Substituting the given values, we get: w^2 + (2w + 4)^2 = 26^2. Solving this equation will give us the values of w and (2w + 4), which are the width and length of the rug, respectively.