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.

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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