Question

The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?

Answer 1

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