Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.

Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)

Feet of fencing = n
Perimeter of square garden = n

Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16

Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d

Divide body tissues by pi:
d = n/pi

Radius = n/2pi

Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2

Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56

The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.

Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380

Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380

Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9

Nearest foot = 284