### Home > ACC6 > Chapter 5 Unit 5 > Lesson CC1: 5.1.3 > Problem 5-28

5-28.

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.

3 cm | A Rectangle 3 centimeters by 6 centimeters |

6 cm |

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.