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Sagot :
Scale factor is the ratio of representation measurement of the figure to the original figures.
The actual dimensions of the kitchen is 12 ft by 14 ft.
What is scale factor?
Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures.
Given information-
Dimensions of the balcony of the apartment is 4 ft by 7 ft or 48 in by 84 in (multiplying it by 12 to convert in inches).
Dimensions of the balcony of the apartment is 0.8 ft by 1.4 in on the scale of drawing.
Dimensions of the kitchen is 2.4 inches by 2.8 inches on the scale of drawing.
The scale factor of the width of the balcony is the ratio of scale dimension of width and the actual dimension of the width . Thus,
[tex]r=\dfrac{0.8}{48} \\r=\dfrac{1}{60}[/tex]
The scale factor of the length of the balcony is the ratio of scale dimension of length and the actual dimension of the length . Thus,
[tex]r=\dfrac{1.4}{84} \\r=\dfrac{1}{60}[/tex]
Thus the scale factor of the length and width of the scale is same which is 1/60.
As the scale is same for the balcony and the kitchen. Thus the scale factor would also be same.
The scale factor of the width of the kitchen is the ratio of scale dimension of width and the actual dimension of the width .
Let the width of the kitchen is x in.Thus
[tex]\dfrac{1}{60}=\dfrac{2.4}{x} \\x=144\rm in[/tex]
Thus the width of the kitchen is 144 in or 12 ft.
The scale factor of the length of the kitchen is the ratio of scale dimension of length and the actual dimension of the length .
Let the length of the kitchen is y in. Thus
[tex]\dfrac{1}{60}=\dfrac{2.8}{y} \\y=168\rm in[/tex]
Thus the length of the kitchen is 168 in or 14 ft.
Hence, the actual dimensions of the kitchen is 12 ft by 14 ft.
Learn more about the scale factor here;
https://brainly.com/question/10253650
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