Question
Given the sum of the perimeters of a square and a circle, prove that the sum of their areas is least when the side of the square is equal to the diameter of the circle.
Solution
Let x be the side of the square and r be the radius of the circle. Let P be the sum of perimeters of square and circle.
...(1)
Let A be the sum of areas of squares and circle
For A to be minimum or minimum,
i.e. side of the square = diameter of circle.
...(1)Let A be the sum of areas of squares and circle
For A to be minimum or minimum,
i.e. side of the square = diameter of circle.
