Question

A piece of wire 12 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. How much wire (in m) should be used for the square in order to minimize the total area?

Answer 1

To minimize the total area, the length of the wire used for the square should be 0 m.

To minimize the total area, we need to find the optimal dimensions for the square. Let's assume one piece of wire is bent into a square and the other piece is bent into a circle. We can use the given wire length of 12 m to solve for the dimensions of the square:

Let the length of one side of the square be 'x'.

Since a square has all sides equal, the total length of the wire used for the square would be 4 times the length of one side: 4x.

Therefore, to minimize the total area, we need to minimize the length of the square's sides:

Answer: To minimize the total area, the length of the wire used for the square should be minimized, which is 0 m.