Answer:
a) A(x)  = 90*x/2  -  x²/2
b) A(max) = 1012.5 m²
Step-by-step explanation:
L = 90 meters of fencing
Rectangular area is 
A(r) = x*y .            where  x  and  y  are the sides of the rectangle
the perimeter is  ( we are going to fence only 3 sides, then)
x + 2*y = 90    or .    y  = ( 90  - x ) /2
Area as a function of x is:
A(x)  = x * ( 90 - x)/2
A(x)  = 90*x/2  -  x²/2
Tacking derivatives on both sides of the equation:
A´(x) =45  -  2*x/2         A´(x) =45  - x
 A´(x) = 0 .      45  - x = 0 .      x  = 45 . meters
and . y   =  ( 90  - x ) 2
y = ( 90- 45 )/2  
y = 22.5 meters
A(max) =  45*22.5  m²
A(max) = 1012.5 m²
If we get the second derivative of A(x) .  A"(x) = - 1       A"(x) < 0
Then A(x) has a maximum for x = 45