Question 746303
using xm for the breadth of the bistro
and l for the length.
l = 160 - 2x for the perimeter.
The area = l x b
         = l x b

        = (160 - 2x)x
     A(x)   = 160x - 2x^2
     A'(x) =  160 - 4x  (Differentiated)

       A'(x) = 0
       160 - 4x = 0
           - 4x = -160
              x = 4

   Using nature table:
                  -  4  +
         160 -4x  +  0  -

 therefore x = 4 is a maximum.

Longest side will be 160 - 4x
                     160 - 16

                      =  144 feet     
Maximum area = 160x - 2x^2
               160(4) - 2(4)^2
                640 - 32
                  608 ft^2