Question 739949
"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."
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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