Respuesta :
Answer:
A(max)  = 1012,5 ft²
Dimensions:
x  =  45 ft
y  =  22,5 ft
Step-by-step explanation:
We have 90 ft of fence
Let call dimensions of rectangular garden  x  and  y  ( x will be the side running parallel to the wall) then
Area of rectangular garden is
A  = x*y   (1)
And perimeter of the rectangular area wich is P = 2*x  * 2*y  and as we will  use fence in only one x side then
P  =  90  =  x  + 2*y   ⇒ y  =  ( 90  -  x  )  / 2
Then equation (1) becomes
A(x)  =  x* ( 90  -  x  )  / 2   ⇒  A(x)  =( 90*x  - x² ) / 2  ⇒  A(x)  =45*x -  x²/2
A(x)  =45*x -  x²/2
Taking derivatives on both sides of the equation
A´(x)  =  45  -  x
A´(x)  =  0    ⇒   45  -  x  =  0
x  =  45 ft
And
y  =  (  90  -  x  ) / 2   ⇒  y  =  ( 90  -  45  )  / 2
y  = 22,5 ft
And th largest possible area is:
A(max)  =  x*y  =  45*22,5
A(max)  = 1012,5 ft²
