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Question -

A wire of length 28 m is to be cut into two pieces. One ofthe pieces is to be made into a square and the other into a circle. What shouldbe the length of the two pieces so that the combined area of the square and thecircle is minimum?



Answer -

Let a piece of length l becut from the given wire to make a square.

Then, the other piece of wire to be madeinto a circle is of length (28 − l) m.

Now, side of square =
Let r bethe radius of the circle. Then,
The combined areas of thesquare and the circle (A) is given by,
Thus, when
By second derivative test,the area (A) is the minimum when.
Hence, the combined area isthe minimum when the length of the wire in making the square iscm while the length of thewire in making the circle is

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