A square piece of card is cut in half and the two pieces placed side by side as shown. 

a. If the large square has a side length of 4a, write an expression for the total perimeter of the two rectangles.

b. One of the two rectangles is halved lengthways and the pieces are also placed side by side.

Write an expression for the total perimeter of the three rectangles. 

c. The three pieces are then arranged in different ways with no gaps between them as shown.

Explain convincingly, using algebra, why the perimeter of the two arrangements is not the same. 

d. Write an expression for the difference in the perimeters of the two arrangements above.

Transcribed Image Text:

4a