Final answer:
To find the width of a rectangle with a perimeter of 48 feet and a length four times its width, set up the equation 2w + 8w = 48, solve for w, and you get the width w = 4.8 feet.
Step-by-step explanation:
The student's question pertains to finding the width of a rectangle when given the perimeter and the relationship between the length and the width. The perimeter of the rectangle is 48 feet, and the length is 4 times the width. To find the width, we can let w represent the width and 4w represent the length. The perimeter of a rectangle is the sum of all its sides, which is 2l + 2w for a rectangle. We can use this information to set up the equation: 2w + 2(4w) = 48.
Solving this equation for w, we combine like terms to get 2w + 8w = 48, which simplifies to 10w = 48. Dividing both sides by 10 gives us w = 4.8. Therefore, the width of the rectangle is 4.8 feet. Please note that proportions such as 1/48 do not apply directly to this problem, as they do not match the given perimeter or the equation needed to solve for the width.