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a wire is 36 meter long is cut into two pieces, each piece is bent to form a rectangle which is 1 centimeter longer that its width. How long should each piece be to minimize the sum of the areas of the two rectangles?

Let x be the length of the first piece. The length of the second piece is 36-x meters.

For simplicity, let d = difference between length and width of rectangles = 1 cm = 0.01 m.

Calculate areas in terms of x and d.

Set the first derivative of total area to 0, then solve for x.

To minimize area of rectangles, both pieces should be 18 meters long.

http://www.flickr.com/photos/dwread/10747170045/

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I double-checked it on a spreadsheet. Minimum total area when the pieces are 18 meters long

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