Final answer:
To find the possible dimensions of the rectangular banner, we can set up an equation using the given information. The width of the banner is 11 ft and the length is 37 ft.
Step-by-step explanation:
To find the possible dimensions of the rectangular banner, we can set up an equation using the given information. Let's assume the width of the banner is 'w'. According to the problem, the length of the banner must be four more than three times the width. So, the length of the banner would be 3w + 4.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the perimeter is given as 96 ft. Setting up the equation, we have 96 = 2((3w + 4) + w).
Simplifying the equation, we get 96 = 2(4w + 4), which further simplifies to 96 = 8w + 8. Now, we can solve this equation to find the possible dimensions of the banner.
Subtracting 8 from both sides, we get 88 = 8w. Dividing both sides by 8, we get w = 11. This means the width of the banner is 11 ft.
Now, substituting the value of w back into the equation for the length, we find the length of the banner to be 3(11) + 4 = 33 + 4 = 37 ft.
So, the possible dimensions of the banner are 11 ft by 37 ft.