### Home > MC2 > Chapter 4 > Lesson 4.2.1 > Problem 4-33

Sophie claims that whenever she increases the perimeter of a rectangle, its area increases.

She showed the rectangle at right and said, “

*If I make the base twice as long, then the area increases.*” Is her statement correct for this figure? Draw a diagram of the rectangle she described and explain whether the area is greater or less than the rectangle at right.Is her claim about the relationship of area and perimeter correct for all figures? For example, is there any way that she could have a rectangle with a greater perimeter than the figure in part (a) but with the same area? Give examples and explain your reasoning.

3 cm | A Rectangle 3 centimeters by 6 centimeters |

6 cm |

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