In this section you will "build" similar rectangles with virtual toothpicks and compare their perimeters.

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Use the toothpick applet to build rectangles, and fill in the data table below the applet. You may copy and paste the table into a Word document. You may also construct a table in your math notebook.

Directions for rectangles you are going to build using the Toothpick Activity.

Make sure the grid is set up for you to use by selecting the Show Grid and Snap to Grid boxes.
Click on the box of toothpicks to choose a toothpick.
Use your mouse to move the toothpicks on the grid.
Right click the toothpick twice or press "r" on your keyboard twice to rotate the toothpick vertically.

Source: University of Illinois

Below is an example of two similar rectangles created with toothpicks. This example is used to fill in the first row of the table for you. You may need to click the "Start Over" button to clear the grid before constructing the larger dilated rectangles.

Two similar rectangles drawn using toothpicks

Dimensions of Original Rectangle	Dimensions of Dilated Rectangle	Scale Factor of Dimensions	Perimeter of Original Rectangle	Perimeter of Dilated Rectangle	Scale Factor of Perimeter
8 toothpicks 2 toothpicks	4 toothpicks 1 toothpick	1 over 2 1 2	20 toothpicks	10 toothpicks	1 over 2 1 2
4 toothpicks 3 toothpicks	8 toothpicks 6 toothpicks
2 toothpicks 1 toothpick	6 toothpicks 3 toothpicks
2 toothpicks 2 toothpicks	8 toothpicks 8 toothpicks
2 toothpicks 3 toothpicks	4 toothpicks 6 toothpicks

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Click here to see an answer

What relationship do you see between the scale factor of the perimeter and the scale factor of the dimensions for each of the 5 pairs of rectangles you constructed?

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Check Your Answer

The scale factor of the perimeter is the same as the scale factor of the dimensions.

Practice

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