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12 October, 09:43

The floor plan of a ballroom is shown at right. The scale is 3 centimeters : 4 meters.

12cm

♒9 cm

1) what are the length and width of the ballroom

2) find the ballroom's area

3) Show that the ratio of the areas is equal to the square of the ratio of the lengths.

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Answers (1)
  1. 12 October, 10:01
    0
    Given:

    scale: 3 cm : 4 m

    Length 12 cm

    Width 9 cm

    We need to convert cm to m.

    length: 12cm / 3cm * 4m = 4 * 4m = 16 meters

    width: 9cm / 3cm * 4m = 3 * 4m = 12 meters

    Area = length * width

    Area = 16 m * 12 m

    Area = 192m²

    Area in cm: 12 cm * 9 cm

    Area in cm: 108 cm²

    cm : m ⇒ ratio format

    ratio: a:b = c:d where ad = bc

    108 : 192 = 12² : 16²

    108 : 192 = 144 : 256

    a = 108; b = 192; c = 144; d = 256

    108 * 256 = 192 * 144

    27,648 = 27,648
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