# Given the sum of

Let us say the sum of perimeter of square and circumference of circle be L

Given: Sum of the perimeters of a square and a circle.

Assuming, side of square = a and radius of circle = r

Then, L = 4a + 2πr …1

Let the sum of area of square and circle be S

So, S = a2 + πr2 S = Condition for maxima and minima  = 0      So, for   >0

This is the condition for minima

From equation 1 Substituting from equation 2    a = 2r

Hence, proved.

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