the areas of two circles are in the ratio 1625 find the ratio of their circumference.
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0
Answer:
Let the radii of the circles be r
1
& r
2
respectively.
Then, their circumferences are 2πr
1
& 2πr
2
, respectively.
So, their ratio=2πr
1
:2πr
2
=r
1
:r
2
.
Again, the areas of the circles are π(r
1
)
2
& π(r
2
)
2
.
Then, their ratio =π(r
1
)
2
:π(r
2
)
2
=(r
1
)
2
:(r
2
)
2
=16:25 ...(given).
∴(r
1
):(r
2
)=
16:25
=±(4:5)
We reject the negative value of r's since the radius is a length.
∴(r
1
):(r
2
)=(4:5).
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