SOLUTION: The areas of two circles are in the ratio 25:64. Find the ratio of their radii.

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Question 126676: The areas of two circles are in the ratio 25:64. Find the ratio of their radii.

Found 2 solutions by solver91311, edjones:
Answer by solver91311(12126) About Me  (Show Source):
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A%5B1%5D=pi%2Ar%5B1%5D%5E2 and A%5B2%5D=pi%2Ar%5B2%5D%5E2. But we are given that A%5B1%5D%2FA%5B2%5D=25%2F64, so we can say:

%28pi%2Ar%5B1%5D%5E2%29%2F%28pi%2Ar%5B2%5D%5E2%29=25%2F64

pi%2Fpi=1 so

%28r%5B1%5D%5E2%29%2F%28r%5B2%5D%5E2%29=25%2F64

Take the square root of both sides:
sqrt%28%28r%5B1%5D%5E2%29%2F%28r%5B2%5D%5E2%29%29=sqrt%2825%2F64%29

r%5B1%5D%2Fr%5B2%5D=5%2F16


Which is the required ratio.

Answer by edjones(7311) About Me  (Show Source):
You can put this solution on YOUR website!
A=pi%2Ar%5E2
.
cross+%28pi%29%2Ar%5B1%5D%5E2%2F%28cross+%28pi%29%2Ar%5B2%5D%29
Therefore:
r%5B1%5D%5E2%2Fr%5B2%5D%5E2=25%2F64
and:
r%5B1%5D%2Fr%5B2%5D=5%2F8 Take the square root of each side.