a) The length and width of the ballroom are 16 meters and 12 meters, respectively.
b) The area of the ballroom is 192 square meters.
c) The ratio of the areas is equal to the square of the ratio of the lengths.
How to analyze the characteristics of the floor of a ballroom by scale factors
Scale factor (r) is defined as the ratio of the real distance (D), in meters, to the scale distance (d), in meters. The area of the floor plan of the ballroom (A) is equal to the product of its width (w) and length (L).
a) The length and width of the ballroom are, respectively:
L = (4 m/3 cm) · (12 cm)
L = 16 m
w = (4 m/3 cm) · (9 cm)
w = 12 m
The length and width of the ballroom are 16 meters and 12 meters, respectively. [tex]\blacksquare[/tex]
b) The ballroom's area is now calculated:
A = (16 m) · (12 m)
A = 192 m²
The area of the ballroom is 192 square meters. [tex]\blacksquare[/tex]
c) The real area is found by applying definitions of ratio and area:
A = (r · w') · (r · L')
A = r² · (w' · L')
The ratio of the areas is equal to the square of the ratio of the lengths. [tex]\blacksquare[/tex]
To learn more on scale factors, we kindly invite to check this verified question: https://brainly.com/question/22312172
