Question

We have two circles A and X. The radius and perimeter of the circle A are b and c respectively.

The radius and perimeter of the circle X are y and z respectively. Consider the following ratios
K=c/b and L=Z/y.
Which of the following statements is true? *
K>L
K K=L
K=2L

Answer 1

`K = L`

Explanation:

Given

Circle A

`r = b` --- radius

`p = c` ---- perimeter

Circle B

`r = y` --- radius

`p =z` --- perimeter

`K = (c)/(b)`

`L = (z)/(y)`

Required

Select the true option

The perimeter of a circle is:

`Perimeter = 2\pi r` ------ the circumference

So, we have:

`c = 2\pi b` --- circle A

`z = 2\pi y` --- circle B

Calculate K

`K = (c)/(b)`

`K = (2\pi b)/(b)`

`K = 2\pi`

Calculate L

`L = (z)/(y)`

`L = (2\pi y)/(y)`

`L = 2\pi`

So, we have:

`K = L = 2\pi`