Question

The perimeter of a rectangle changes from 2.5 to 10 after a dilation. What was the scale factor of the dilation?

2
4
7.5
12.5

Answer 1

scale factor = new length/old length

scale factor = 10/2.5 = 4

The scale factor is 4.

Answer 2

B. 4

Explanation:

Let x be the scale factor of the given dilation.

We have been given that the perimeter of a rectangle changes from 2.5 to 10 after a dilation. We are asked to find the scale factor of dilation.

The scale factor multiplied by the original side gives the length of new side after dilation, so we can set an equation as:

`\text{Original length }\cdot \text{Scale factor}=\text{New length after dilation}`

Upon substituting our given values in above equation we will get,

`2.5\cdot x=10`

Upon dividing both sides of our equation by 2.5 we will get,

`(2.5\cdot x)/(2.5)=(10)/(2.5)`

`x=4`

Therefore, the scale factor of the given dilation is 4 and option B is the correct choice.