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Cerrena [4.2K]
3 years ago
14

The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting a

rea. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
Mathematics
1 answer:
kykrilka [37]3 years ago
8 0
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
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