Question

The ratio of the diameters of two circles is y:z. What is the scale factor of the circles?

Answer 1

Scale factor is based on the radii of two circles. So each radius for your two circles are y/2 and z/2. The scale factor would just be the ratio of the radii, so it would be
`((y)/(2))/((z)/(2))=(y)/(z)`

Answer 2

The scale factor is
`(y)/(z)`

Explanation:

Given: Ratio of diameter of 2 circles which is y : z

To find: Scale Factor of the circles

Scale factor of circles is the ratio of their radii.

let, a is the same multiple which given exact value of diameter

⇒ The diameter of 1st circle = ya

⇒ Radius of 1st circle =
`(ya)/(2)`

⇒ The diameter of 2nd circle = za

⇒ Radius of 2nd circle =
`(za)/(2)`

So, The scale factor =
`(Radius\: of\: 1st\: circle)/(Radius\: of\: 2nd\: circle)`

=
`((ya)/(2))/((za)/(2))`

=
`(ya)/(2)*(2)/(za)}`

=
`(y)/(z)`

Therefore, The scale factor is
`(y)/(z)`