Question

Given the sum of the perimeters of a square and a circle, show that the sum of their areas is least when one side of the square is equal to diameter of the circle.

Answer 1

Let `S = 4x + 2piy`. Then, `y = ((S - 4x))/(2pi))`
Let `A = x^(2) + pi y^(2)`. Then, `A = x^(2) + ((S -4x)^(2))/(4pi)`