SOLUTION: This problem includes "Pie"=3.14. I can't find a way to symbolize "pie". I hope this doesn't affect your ability to help. Also this is part of factoring polynomials. "The sum of

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This problem includes "Pie"=3.14. I can't find a way to symbolize "pie". I hope this doesn't affect your ability to help. Also this is part of factoring polynomials. "The sum of      Log On


   

Question 739949: This problem includes "Pie"=3.14. I can't find a way to symbolize "pie". I hope this doesn't affect your ability to help. Also this is part of factoring polynomials.
"The sum of the areas of two circles is 169pie square inches. the length of a radius of the smaller circle is 7 inches less than the length of a radius of the larger circle. Find the length of the larger circle."
I am not sure how to set this problem up to solve it. I don't remember how to find the area of a circle.
Any step by step help would be appreciated. thank you!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of the areas of two circles is 169pie square inches. the length of a radius of the smaller circle is 7 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle."
***
area of a circle=πr^2
let r=radius of larger circle
area of larger circle=πr^2
r-7=radius of smaller circle
area of smaller circle=π(r-7)^2
sum of the areas of two circles is 169pie square inches
πr^2+π(r-7)^2=169π
factor out π
r^2+(r-7)^2=169
r^2+r^2-14r+49=169
2r^2-14r-120=0
r^2-7r-60=0
(r+5)(r-12)=0
r=-5 (reject, r>0)
or
r=12
r-7=5
radius of larger circle=12 sq in
radius of smaller circle=5 sq in