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