32. Think About a Plan Two similar rectangles have areas 27   in . 2 27 in , . squared  and 48   in . 2 . 48 in , . squared , .  The length of one side of the larger rectangle is 16 in. What are the dimensions of both rectangles?
    • How does the ratio of the similar rectangles compare to their scale factor?
    • How can you use the dimensions of the larger rectangle to find the dimensions of the smaller rectangle?
33. The longer sides of a parallelogram are 5 m. The longer sides of a similar parallelogram are 15 m. The area of the smaller parallelogram is 28   m 2 . 28 , m squared , .  What is the area of the larger parallelogram?

Algebra Find the values of x and y when the smaller triangle shown here has the given area.

34. 3   cm 2 3 , cm squared
35. 6   cm 2 6 , cm squared
36. 12   cm 2 12 , cm squared
37. 16   cm 2 16 , cm squared
38. 24   cm 2 24 , cm squared
39. 48   cm 2 48 , cm squared
40. Medicine For some medical imaging, the scale of the image is 3 : 1. That means that if an image is 3 cm long, the corresponding length on the person's body is 1 cm. Find the actual area of a lesion if its image has area 2 . 7   cm 2 . 2 . 7 , cm squared , .
41. In Δ R S T ,   R S = 20   m , S T = 25   m , cap delta r s t comma r s . equals 20 m comma s t equals 25 m comma  and R T = 40   m . r t equals 40 m .
    1. Open-Ended Choose a convenient scale. Then use a ruler and compass to draw Δ R ′ S ′ T ′ ∼ Δ R S T . cap delta r , prime s . prime t prime tilde operator . cap delta r s t .
    2. Constructions Construct an altitude of Δ R ′ S ′ T ′ cap delta r , prime s . prime t prime  and measure its length. Find the area of Δ R ′ S ′ T ′ . cap delta r , prime s . prime t prime .
    3. Estimation Estimate the area of Δ R S T . cap delta r s t .

Compare the blue figure to the red figure. Find the ratios of (a) their perimeters and (b) their areas.

42. 
43. 
44. 
45. 1. Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest radical form.
    2. Use your answer to part (a) and Theorem 10-7 to find the areas of the regular hexagons shown below.

    

46. Writing The enrollment at an elementary school is going to increase from 200 students to 395 students. A parents' group is planning to increase the 100 ft-by-200 ft playground area to a larger area that is 200 ft by 400 ft. What would you tell the parents' group when they ask your opinion about whether the new playground will be large enough?

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