SOLUTION: The diameters of 2 circles are in the ratio 3:4 and the sum of their areas is equal to the area of a circle whose diameter measure 30m. Find the diameters of the 2 circles. A=

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Question 838484: The diameters of 2 circles are in the ratio 3:4 and the sum of their areas is equal to the area of a circle whose diameter measure 30m. Find the diameters of the 2 circles.
A= 706.5
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The diameters of 2 circles are in the ratio 3:4 and the sum of their areas is equal to the area of a circle whose diameter measure 30m.
Find the diameters of the 2 circles.
:
Their radii will also have a 3:4 ratio
let x = the multiplier
then
3x = the radius on one circle
and
4x = the radius of the other
:
%28pi%2A%283x%29%5E2%29+%2B+%28pi%2A%284x%29%5E2%29 = pi%2A15%5E2
divide thru by pi
9x^2 + 16x^2 = 225
25x^2 = 225
divide both sides by 25
x^2 = 9
x = 3 is the multiplier
then
3(3) = 9 is the radius of the 1st circle; diameter is 18
and
4(3) = 12 is the radius of the 2nd circle; diameter is 24