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zhuklara [117]
3 years ago
15

Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 28 meters

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
3 0
The perimeter is given by:
 P = 2x + 2y = 28
 The area is given by:
 A = x * y
 Writing the area based on x we have:
 A (x) = x * (14-x)
 Rewriting:
 A (x) = 14x-x ^ 2
 Deriving we have:
 A '(x) = 14-2x
 We equal zero and clear x:
 14-2x = 0
 x = 14/2
 x = 7
 We are now looking for the other dimension:
 y = 14-x
 y = 14-7
 y = 7
 Answer: The length and width of a rectangle that has the given perimeter and a maximum area are:
 
y = 7 meters
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