keven9110 keven9110
  • 26-03-2018
  • Mathematics
contestada

Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 244 meters

Respuesta :

calculista
calculista calculista
  • 04-04-2018
we know that

[perimeter of rectangle]=2*(length+width)

Let
x-----------> length
y-----------> width
so
P=2*(x+y)-----------> 244=2*(x+y)-----> x+y=122-------> y=122-x

Area=x*y-------> x*(122-x)----> 122x-x²

find the derivative function and equals to zero

122-2x=0-----> 122=2x----------> x=61 m
y=122-x------> y=122-61---------> y=61 m

the maximum area is given by a square

the answer is
is a square of side 61 m


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