Question 317038
For a rectangle, the area is,
{{{A=L*W=225}}}
and the perimeter is,
{{{P=2(L+W)}}}
From the area equation,
{{{L=225/W}}}
Substitute into the P equation,
{{{P=2(225/W+W)=450/W+2W}}}
Now P is a function of only one variable.
Take the derivative and set it equal to zero to find extrema.
{{{dP/dW=-450/W^2+2=0}}}
{{{450/W^2=2}}}
{{{W^2=450/2=225}}}
{{{W=15}}}
{{{L=225/15=15}}}
The rectangle with the minimum perimeter is a square with side 15 cm.
{{{P=4s=4(15)}}} 
{{{highlight(P=60)}}} cm.