Question 148005
Let {{{r[1]}}}=radius of first circle and {{{r[2]}}}=radius of second circle


Since the "radius of a circle is 1 meter longer than the radius of another circle", this means that {{{r[1]=r[2]+1}}}


So the area of the first circle is 

{{{A[1]=pi*r[1]^2}}}



{{{A[1]=pi*(r[2]+1)^2}}} Plug in {{{r[1]=r[2]+1}}}



{{{A[1]=pi*(r[2]^2+2r[2]+1)}}} Foil




The area of the second circle is 


{{{A[2]=pi*r[2]^2}}}



Since "their areas differ by 5 pie square meters", this means that 


{{{A[1]-A[2]=5pi}}}



{{{pi*(r[2]^2+2r[2]+1)-(pi*r[2]^2)=5pi}}} Plug in {{{A[1]=pi*(r[2]^2+2r[2]+1)}}} and {{{A[2]=pi*r[2]^2}}}



{{{pi(r[2]^2+2r[2]+1-r[2]^2)=5pi}}} Factor out the GCF {{{pi}}}



{{{cross(pi)(r[2]^2+2r[2]+1-r[2]^2)=5cross(pi)}}} Divide both sides by {{{pi}}}



{{{r[2]^2+2r[2]+1-r[2]^2=5}}} Simplify



{{{2r[2]+1=5}}} Combine like terms.



{{{r[2]=(4)/(2)}}} Divide both sides by {{{2}}} to isolate {{{r[2]}}}.



{{{r[2]=2}}} Reduce.



So the radius of the second circle is 2 meters.



{{{r[1]=r[2]+1}}} Go back to the first equation



{{{r[1]=2+1}}} Plug in {{{r[2]=2}}}



{{{r[1]=3}}} Add.




So the radius of the first circle is 3 meters.



note: the two radii can be switched since the problem does not specifically mention the "first" circle or the "second" circle.