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The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

#### Options

3 : 2

4 : 9

2 : 3

81 : 16

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#### Solution

Let the the radii of the two circles be r and R, the circumferences of the circles be c and C and the areas of the two circles be a and A.

Now,

`"a"/"A" = 9/4`

`=>(pi"r"^2)/(pi"R"^2) = (3/2)^2`

`=>"r"/"R" = 3/2`

Now, the ratio between their circumferences is given by

`c/C = (2pi"r")/(2pi"R")`

`="r"/"R"`

`=3/2`

Hence, the correct answer is option (a)

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