show that it is impossible to form a 20 cm length of wire into rectangle with area 30 cm^2.

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A rectangle is formed with a wire that has a length of 20 cm. Let the length of the rectangle be x. The width is (20 - 2x)/2 = 10 - x

The area of the rectangle is A = x*(10 - x) = 10x - x^2

To maximize A, solve A' = 0

A' = ` `10 - 2x

10 - 2x = 0

=> x = 5

The length of the rectangle is 5 and the width is 5 which gives a maximum area of 25 cm^2.

This proves that it is not possible to form a rectangle with an area of 30 cm^2 with a wire of length 20 cm.

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