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They can, but at different rates. Consider a square that is 4 units on each side. Its area is 4 x 4 = 16 units. Its perimeter is 4 + 4 + 4 + 4 = 16 units. Nice coincidence! Then consider increasing the square's size to 6 units on each side. Its area would then be 6 x 6 = 36 units. Its perimeter would be 6 + 6 + 6 + 6 = 24 units. So an increase in perimeter of 8 units (24 - 16) resulted in an increase in area of 20 units (36 - 16).

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Q: Do both area and perimeter increase together?
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