SOLUTION: The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles. If the value of A is 2

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Question 366921: The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles.
If the value of A is 20π;, calculate the radius of each circle.
Answer by mananth(16946) (Show Source):
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The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles.
radius = x
Area = pi*x^2
other radius = 6-x
area = pi*(6-x)^2
..
A= pix^2+pi(6-x)^2
A= pi(x^2+(6-x)^2)
A= pi(x^2+36-12x+x^2)
A=pi(2x^2-12x+36)
A=2pi(x^2-6x+18)
.........
20pi =2pi(x^2-6x+18)
/2pi
10=(x^2-6x+18)
x^2-6x+8=0
(x-4)(x-2)=0
x= 2 OR 4
..
2 & 4 are the radii
...
m.ananth@hotmail.ca