In this section, you will use an interactive applet to build a series of rectangles.

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Click the image below to open an applet to investigate how using a scale factor affects the area of similar rectangles. Use the applet to complete the table below, and then use your table to answer the questions that follow.

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Click here for directions to use the applet

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Poster and photograph with dimensions labeled

Length A

Height A

Scale Factor

Number of Rectangle A inside Rectangle B

Length B over Length A Length B Length A

 Height B over Height A Height B Height A

Area B over Area A Area B Area A

53

28

4

16

4

4

16

53

28

3

 

 

 

 

53

28

5

 

 

 

 

19

38

3

 

 

 

 

35

38

3

 

 

 

 

35

45

3

 

 

 

 

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How does the Scale Factor compare to the ratio Length B over Length A Length B Length A ?
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The Scale Factor is equal to the ratio of Length B to Length A.Close Pop Up

How does the Scale Factor compare to the ratio Height B over Height A Height B Height A ?
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The Scale Factor is equal to the ratio of Height B to Height A.Close Pop Up


How does the Scale Factor compare to the ratio Area B over Area A Area B Area A ?
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The ratio of Area B to Area A is equal to the square of the Scale Factor.Close Pop Up


How does the Number of Rectangle A’s that appear to fit inside Rectangle B compare to the Scale Factor?

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The Number of Rectangle A’s that appear to fit inside Rectangle B is equal to the square of the Scale Factor.Close Pop Up

Is the relationship you have observed between the ratio Area B over Area A Area B Area A and the Scale Factor true for different scale factors? How do you know? Confirm your answer using additional scale factors for the same Rectangle A in the applet.

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Yes. In each row with different scale factors, the ratio of Area B to Area A is equal to the square of the scale factor. Using Scale Factors between 1.0 and 6.0 in the applet supports this observation. Close Pop Up

Is the relationship you have observed between the ratio Area B over Area A Area B Area A and the Scale Factor true for different combinations of lengths and widths? How do you know?

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Yes. In each row with the same scale factor but different lengths and widths, the ratio of Area B to Area A is equal to the square of the scale factor. Using several different combinations of length and width in the applet supports this observation.Close Pop Up

Practice

  1. Rectangle QUAD is dilated by the scale factors shown. Identify the changes in the area of Rectangle QUAD that will result from the dilation. Drag the description of the changes in the area to the box next to the scale factor.

    2. Interactive exercise. Assistance may be required.

  2. Rectangle QRST is similar to rectangle GHJK. If the area of rectangle QRST is 131 over 2 1 2 square inches, what is the area of rectangle GHJK?

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    Hint

    What is the ratio of the corresponding sides?
    Square this number to determine the ratio of the areas.Close Pop Up

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    Check Your Answer

    131 over 2 1 2 x (2)2 = 131 over 2 1 2 x 4 = 54 square inchesClose Pop Up