Answer
$40$
Work Step by Step
We are given that $xy=100 ~~~(a)$
Here, we have: $\ Perimeter =2(x+y)~~~~(b)$
where, $x$ and $y$ represents length and breadth.
Next, $y=\dfrac{100}{x} ~~~(c)$
and $ P=2x+\dfrac{(2)(100)}{x}=2x+\dfrac{200}{x}~~~(d)$
For minimum perimeter , we must have $\dfrac{dP}{dx}=0$
or, $2-\dfrac{200}{x^2}=0 \\ x^2=100 \\ x=10$
Now, equation $c$ becomes: $y=10$
Thus, the minimum perimeter is: $P_{min}=2(10+10)=40$
