Length of the rectangular acting area be x.Width = 42 / xWe asked to find the perimeter ( the number of yard that are needed to enclose the area)P = 2(length + width) = 2(x + 42/x) = 2x + 84/x
The perimeter is minimum when the differentiation is equal to 0.2 - 84/x^2 = 02x^2 - 84 = 0x^2 = 42 x = 6.48
Thus, the minimum yards of string lights the manager need to enclose the area is 2(6.48) + 84 / 6.48^2 = 12.96 + 12.96 = 25.92 so it is approximately 26 yards
