Randy is building a fence at the side of his warehouse. He has 120 m of fencing and plans to use the side of the warehouse as one side of the rectangular fenced area. What are the dimensions of the
maximum area Randy can enclose?

The width (side perpedicular to the wall of the werehouse):  x = 30 m

The lenght (side parallel to the wall of the werehouse):  y = 60 m

Step-by-step explanation:

x - the width of the fenced area

Randy has 120 m of fencing so for the lenght remain (120-2x) m of fencing:

y = 120 - 2x

Area of the fencing:  A = x•y

A(x) = x•(120 - 2x)

A(x) = -2x² + 120x              ←  quadratic function

The maximum value of quadratic function occurs at:  

a = -2     b = 120

y = 120 - 2•30 = 60

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step-by-step explanation: