Equivalent Scale Factor

A scale area is a number which scales, or multiplies, some quantity. In the equation y=Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a equivalent scale factor of 2 for distance, while cutting a cake in half results in pieces with a scale factor of ½.
SOURCE: WIKIPEDIA

Example problems of equivalent scale factor:

Equivalent scale factor problem 1:
Find the scale factor to the following figure:

Equivalent scale factor solution:
If we want to find the length of smaller rectangle then we can multiply the length of the one side of larger rectangle and the value of scale factor.
We can find the scale factor of the given rectangles by using the following formula,
Let D_l be the dimensions of larger rectangle and D_s be the dimensions of smaller rectangle and s be the scale factor.
Therefore the formula as,
                D_l*s=D_s
Substitute the values of dimensions into the above formula. Then we get
                  30*s=24
Divide by the value 30 on both sides,
                   `(30s)/30` `=` `24/30`
                       ` s ` `=` `24/30`
Divide by the value of 6 on both numerator and denominator. Then we get the value of scale factor.
                        s = `4/5 ` or 4:5
Therefore scale factor of smaller to larger rectangle= 4:5
Answer: 4:5
Equivalent scale factor problem 2:
Find the larger to smaller scale factor for the following figure:

Equivalent scale factor solution:
If we want to find the length of smaller rectangle then we can multiply the length of the one side of larger rectangle and the value of scale factor.
We can find the scale factor of the given rectangles by using the following formula,
Let D_l be the dimensions of larger rectangle and D_s be the dimensions of smaller rectangle and s be the scale factor.
Therefore the formula as,
                D_l*s=D_s
Substitute the values of dimensions into the above formula. Then we get
                  39*s=26
Divide by the value 48 on both sides,
`(39s)/(30)` `=` `26/39`
` s ``=` `26/39`
Divide by the value of 13 on both numerator and denominator. Then we get the value of scale factor.
                        s = `2/3` or 2:3
Therefore scale factor of larger to smaller scale rectangle= 3:2
Answer: 3:2

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Practice problems of equivalent scale factor:

1. Find the scale factor to the following figure:

2. Find the larger to smaller scale factor for the following figure:

Answer:
1. 3:4
2: 6:5