Question

Show that of all the rectangles of given area, the square has the smallest perimeter.

Answer 1

Let x and, y be the lengths of sides of a rectangle. Again let A denote its area and P be the perimeter. 

Now,area  of reactangle, A = xy

Here, x and A and area of rectangle can never be negative. So, P is minimum. 

Hence, perimeter of rectangle is minimum, when rectangle is a square.