To find the perimeter of the tabletop, we need to know the length of each side of the square. We can use the formula for the area of a square to find this length:
Area = side^2
We are given the area of the tabletop as 64x48x + 9, so we can set up the following equation:
64x48x + 9 = side^2
Simplifying the left-hand side:
64x48x + 9 = (8x6x)^2 + 3^2
64x48x + 9 = 36^2 + 3^2
64x48x + 9 = 1296 + 9
64x48x = 1296
Dividing both sides by 64x48:
side^2 = 27
Taking the square root of both sides, we get:
side = sqrt(27)
Now we know the length of one side of the square tabletop, and since all sides are equal, the perimeter is:
Perimeter = 4 x side
Perimeter = 4 x sqrt(27)
Perimeter = 4 x 3sqrt(3)
Perimeter = 12sqrt(3)
Therefore, the perimeter of the tabletop is 12sqrt(3) units.