Final answer:
To find the length and width of the rectangle, we set up an equation based on the given information. Solving this equation, we find that the width of the rectangle is approximately 5.69 inches and the length is approximately 9.69 inches.
Step-by-step explanation:
To solve this problem, we first need to set up equations based on the given information. Let's call the width of the rectangle 'w' inches. According to the problem, the length of the rectangle is 4 inches more than its width, so we can write the length as 'w + 4' inches.
The area of a rectangle is equal to the length multiplied by the width, so we can write the equation: 'w * (w + 4) = 5 + 2 * (2w + 2w + 4)'
Simplifying the equation, we get 'w^2 + 4w = 5 + 8w + 8'
Continuing to simplify, we have 'w^2 - 4w - 13 = 0'
At this point, we can solve the quadratic equation using factoring, completing the square, or the quadratic formula. The solutions are approximately 'w = -1.69' and 'w = 5.69', but since we're dealing with lengths, the width cannot be negative. So, the width of the rectangle is approximately 'w = 5.69' inches, and the length is 'w + 4 = 9.69' inches.