**Introduction for scale factor formula:**

The scale factor is two or more diagrams are same, then their sizes can be compared. The scale factor is defined as the ratio of length of one side of one diagram to the length of the corresponding side of the other diagram. The following formula used to find the scale factor. Let us learn about the scale factor and its formula.

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A scale factor is defined as a number which scales, or multiplies, some quantity. Consider the equation

** y = Cx**

Here *C* is the scale factor for *x*. *C* is also the coefficient of *x*, and it is called as the constant of proportionality of *y* to *x*. This is the formula for Scale Factor.

Let us consider an example, doubling distances corresponds to a scale factor of 2 for distance, while cutting a cake in half results in pieces with a scale factor of `(1)/(2)` .

**Formula Using Multiplication to find a scale factor:**

Consider the shape of an object that is drawn to a certain scale.

Here the scale factor is nothing but the dimension of the actual object to the dimension that has been drawn

Consider a problem 5 * 2 = 10

Here the value 10 has been obtained by multiplying 5 by 2

Hence 2 is the scale factor of 5

If a quantity is multiplied by a certain number then that number is said to be the scale factor

Let us consider , If the side of a square ABCD is 6m. Find the side of square PQRS if scale factor is 12

** Solution:**

Let S be the side of square,

S_{ABCD } = 6cm

Scale factor = 12

Using Formula,

S_{PQRS }= 12 x S_{ABCD }

= 12 x 5

= 60cm

In other words scale factor is just a ratio of two directly related quantities.

For example if the height of the person is 2m and the shadow is 8m long

Then the scale factor is given by

Scale factor = `8/2`

Thus you can get some ideas about the scale factor formula.