document.write( "Question 679452: How do I solve this?
\n" ); document.write( "Q. Given two concentric circles, find the length of the radius of the inner circle.\r
\n" ); document.write( "\n" ); document.write( "knowns:
\n" ); document.write( "Area of the annulus is 40pi square inches.
\n" ); document.write( "The radius of the outer circle is (one inch plus two times the radius of the inner circle). \n" ); document.write( "
Algebra.Com's Answer #421961 by DrBeeee(684)\"\" \"About 
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Let r = the radius of the inner circle.
\n" ); document.write( "Then the radius of the outer circle is
\n" ); document.write( "(1) radius of outer = (1 + 2r)
\n" ); document.write( "Using the formula for the area of a circle (pi*radius^2), and taking the difference between the outer circle area and inner circle area gives us
\n" ); document.write( "(2) 40pi = pi*((1+2r)^2 - r^2) which reduces to
\n" ); document.write( "(3) 40 = 1 + 4r + 4r^2 - r^2 or
\n" ); document.write( "(4) 3r^2 + 4r - 39 = 0 which factors into
\n" ); document.write( "(5) (3r + 13)*(r - 3) = 0, which gives the roots
\n" ); document.write( "(6) r = (-13/3, 3)
\n" ); document.write( "Since the radius must be positive we select
\n" ); document.write( "(7) r = 3
\n" ); document.write( "Let's see if this is correct using (2)
\n" ); document.write( "Is (40pi = pi*((1+2*3)^2 - 3^2))?
\n" ); document.write( "Is (40pi = pi*(49 - 9))?
\n" ); document.write( "Is (40pi = 40pi)? Yes
\n" ); document.write( "Answer: The radius of the inner circle is 3 inches. \n" ); document.write( "
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