Question 1076116
Dimensions x and y.


Perimeter:  {{{2(x+y)=30}}}
{{{x+y=15}}}
{{{y=15-x}}}


Area:  {{{xy}}}
{{{x(15-x)}}}
Variable A for area, {{{A(x)=x(15-x)}}}

A can take the form of a parabola if graphed.  
A(x)=x(15-x) has when multiplied, an {{{-x^2}}} term so the parabola has a maximum point exactly in the middle of the Zeros of A.


{{{x(15-x)=0}}}
{{{system(x=0,or,x=15)}}}


The maximum area will be {{{x=(15+0)/2=7&1/2}}}


Now find y.
{{{y=7&1/2}}}



Both x and y are each  {{{7&1/2}}}.
This is a square shape.


{{{A(7.5)=(7.5)^2}}}
{{{A(7.5)=highlight(56&1/4)}}}