Final answer:
To find the greatest rectangular dance area possible with the stage forming one of the sides, we use the perimeter formula and assume the stage forms one of the shorter sides. By solving the equation 2x + 2y = 48, we find that the dimensions of the rectangle are 12 feet by 12 feet.
Step-by-step explanation:
To find the greatest rectangular dance area possible with the stage forming one of the sides, we need to consider that the total length of the fencing is 48 feet. Let's assume that the stage forms one of the shorter sides of the rectangle.
If the stage forms one of the shorter sides, we'll call its length x and the length of the longer side y.
The perimeter of a rectangle is given by the formula P = 2x + 2y. In this case, 2x + 2y = 48.
Since the stage forms one of the shorter sides, we know that x = y.
Substituting y for x in the equation 2x + 2y = 48, we get 4x = 48.
Dividing both sides by 4, we find that x = 12.
So, the greatest rectangular dance area possible with the stage forming one of the sides is a rectangle with sides measuring 12 feet by 12 feet.