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Two signboards, one circular and one square are to be made using a wire of length 40 m and cutting it into two pieces. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

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Total length of wire = 40 m

Let length of two piece of wire is x and (40 - x)m

Perimeter of circle = x = 2πr

Hence combined area is minimum when length of first piece of wire is 40/(4 + π) m and length of second piece of wire is 160/(4 + π) m.

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