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.

Asked by Aaryan | 1 year ago |  135

##### Solution :-

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

= a = $$\dfrac{ (L – 2πr)}{4}$$… (1)

Let the sum of area of square and circle be S

So, S = a2 + πr2  Answered by Sakshi | 1 year ago

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