Q25 of 26 Page 1

A farmer wants to construct a circular garden and a square garden in his field. He wants to keep the sum of their perimeters 600 m. Prove that the sum their areas is the least, when the side of the square garden is double the radius of the circular garden. Do you think that a good planning can save energy, time and money?

Given Data:


A farmer wants to construct a circular garden and a square garden in his field


Sum of the perimeter is 600 m


Calculation:


Let r be the radius of circular field and a be the side of square field


2πr+4a=600



Sum of the areas, S=πr2+a2



Differentiating w.r.t to r



Now



⇒ 4r–300+πr=0



Now find the second derivative to check for maxima and minima





Therefore side a of the square is



a = 2r


Yes good planning can save time, money and energy. This helps in completing the work in minimal resources.


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