Question

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

Answer 1

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