Scale factor is [tex]\frac{14}{21}[/tex].
A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
Given
The rectangle on the right is a scaled copy of the rectangle on the left.
[tex]\frac{42}{63}[/tex] and 15 ÷ [tex]\frac{45}{2}[/tex]
[tex]\frac{42}{63}[/tex]
Rationalizing [tex]\frac{42}{63}[/tex] by 45
= [tex]\frac{42(45)}{63(45)}[/tex]
= [tex]\frac{1890}{2835}[/tex]
15 ÷ [tex]\frac{45}{2}[/tex]
Rationalizing 15 ÷ [tex]\frac{45}{2}[/tex] by 63
= [tex]\frac{30(63)}{45(63)}[/tex]
= [tex]\frac{1890}{2835}[/tex]
If we want to find the scale factor we have to equal the proportions of two rectangles.
∴ Scale factor = [tex]\frac{1890}{2835}[/tex] = [tex]\frac{14}{21}[/tex]
Hence, scale factor is [tex]\frac{14}{21}[/tex].
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