A scale factor allows a shape to be changes into another shape by changing the linear dimensions to the multiples of the initial dimension and a constant
The expression that finds the change in scale factor for the longer pool with a final length of 33 ft. Sierra is building is the option;
- [tex]\dfrac{2 \, ft.}{3 \, ft.}[/tex]
Reason:
Known parameters are;
Dimensions of the pool created = 14 ft. wide × 22 ft. long
Final length of the pool = 33 ft.
Let x represent the length of the drawing using the initial scale factor, we have;
- [tex]The \ initial \ scale \ factor = \dfrac{22 \, ft.}{x \, in.}[/tex]
The scale factor of the drawing following a final length of 33 ft. is therefore;
- [tex]New \ scale \ factor = \dfrac{33 \, ft.}{x \, in.}[/tex]
The change in scale factor is given as follows;
[tex]Change \ in \ scale \ factor = \dfrac{Initial \, scale \, factor}{Final \, scale \, factor}[/tex]
Therefore;
- [tex]Change \ in \ scale \ factor = \frac{\left( \dfrac{22 \, ft.}{x \, in.} \right)}{\left( \dfrac{33 \, ft.}{x \, in.} \right)} = \dfrac{2 \, ft.}{3 \, ft.}[/tex]
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