[size=150]This activity will explore the relationship of the scale factor on the the ratio of the side lengths versus the ratio of the areas.[br][list][*]The slider represents the scale factor of the rectangle on the right to the rectangle on the left (right:left). For example, [math]\alpha=1[/math] means that the side lengths have a ratio of 1:1[/*][*][icon]/images/ggb/toolbar/mode_tool.png[/icon] will allow you to create identical rectangles to that of the rectangle on the left. [br][/*][/list][u]Activity[br][/u][list=1][*]As stated above with [math]\alpha=1[/math], the ratio of the sides is 1:1. What is the ratio of the areas? Why?[/*][*]Move the slider to [math]\alpha=2[/math], then answer the following questions. Answer these same questions then for [math]\alpha=3[/math], [math]\alpha=4[/math], and [math]\alpha=5[/math]. [/*][list][*]What is the scale factor?[/*][*]What is the ratio of the side lengths?[/*][*]Use the [icon]https://www.geogebra.org/images/ggb/toolbar/mode_tool.png[/icon] to create additional rectangles of the left. As you create them, align them inside the rectangle on the right until it is filled. How many of the left rectangles fit inside the right rectangle? What does this tell you about the ratio of the areas of the rectangles?[/*][*]How does the ratio of the areas compare to the ratio of the side lengths?[/*][/list][*]Let's tie it all together! You have examined the relationship of the right rectangle to the left rectangle through five scale factor changes. What can you say is the relationship that exists between the scale factor and the ratio of the side lengths? What can you say is the relationship that exists between the scale factor and the ratio of the areas?[/*][/list][br][/size]