Final answer:
The equation to determine the width (w) of Filipo's sandbox is by setting up the perimeter formula (P = 2l + 2w) with given perimeter of 29 feet, and substituting the relationship between the length and width (l = 2w + 1).
Step-by-step explanation:
To determine the width w of Filipo's sandbox, we can start with the information given that the length (l) is 1 foot longer than twice the width. We can express this as l = 2w + 1. The perimeter (P) of a rectangle is given by P = 2l + 2w. Since we know the perimeter is 29 feet, we can substitute the expression for l into the perimeter formula to find w. The resulting equation is 29 = 4w + 2 + 2w, which simplifies to w = 4.5 feet.
The equation for the perimeter using the given information is:
P = 2(2w + 1) + 2w
Expanding this equation we have:
29 = 4w + 2 + 2w
Combining like terms:
29 = 6w + 2
Subtracting 2 from both sides to solve for w:
27 = 6w
Dividing both sides by 6:
w = 4.5
Therefore, the width of the sandbox is 4.5 feet.