Question 959210
The area of the rectangle is,
{{{A=L*W}}}
The perimeter of the rectangle is fixed at,
{{{P=2L+2W=60}}}
{{{L+W=30}}}
{{{L=30-W}}}
Substituting into the area,
{{{A=(30-W)W}}}
{{{A=30W-W^2}}}
Now the area is the function of only one variable.
We can convert to vertex form to find the maximum value.
{{{A=-W^2+30W}}}
{{{A=-(W^2-30W+225)+225}}}
{{{A=-(W-15)^2+225}}}
So when {{{W=15}}}{{{m}}} the maximum area of {{{225}}}{{{m^2}}} is achieved.
{{{L=30-15}}}
{{{L=15}}}{{{m}}}
So the rectangle that gives the max area is a square of side 15m.