In this activity, you will explore the difference between scaling the sides of a rectangle and scaling the area of a rectangle.

1. Try sliding the X value to scale the sides of the rectangle. What do you notice about the area of the rectangle?
2. What do you need to scale the side lengths by to get an area of 9?
3. Click the "Scale Area" box. Slide the Area dot to adjust the area of the rectangle. How is this affecting the side lengths of the rectangle?
4. Which do you think increases faster, side length or area? Play with both modes and convince yourself.
5. Write down the formula for the area of a rectangle. Using this and your observations, try to create a mathematical relationship between scaling side lengths and scaling area.
6. Test your relationship by experimenting in both modes. Does it hold up?
7. In a few sentences, explain the reasoning behind your relationship and why you believe it did or did not work.