<PRE><B>Question 426053</B>
Solution:Denote the length of rectangle  x m, since the perimeter is 48m then the width of rectangle is (24-x)m. We know that the area of rectangle is:

  {{{A=x*(24-x)}}}

   {{{A=-x^2+24x}}} This function introduce a downward parabola.

We find the vertex of this parabola: {{{x=(-24)/(-2)=12}}}

Since the length is 12m the width will be: 24-12=12m

We conclude that this rectangle has the maximum area when its shape is square of side 12m.

 We  find the value of area for x=12m : {{{A(12)=-(12)^2+24*12}}}

   {{{ A(12)=144 m^2}}}.




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