Question 121910
Here's the solution to the same problem except that the overall length of the wire was different.  I'll let you go through and change the numbers, but this should help you solve your problem.


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Let's say the wire is cut into two pieces, one of them is L inches, and the other is 220 - L inches.


If we take the first piece and form it into a square, each one of the sides of the square will be {{{L/4}}} inches, so the area of the square will be {{{A[s]=(L/4)^2}}}


The area of a circle is given by {{{A[c]=pi*r^2}}}, but since the circumference of a circle is given by {{{C=2*pi*r}}} we can say that the radius of a circle with circumference C is {{{r=C/(2*pi)}}}.


Now we can re-write the circle area formula as {{{A[c]=pi*(C/(2*pi))^2}}}, then simplify to:


{{{A[c]=C^2/(4*pi)}}}


But we know that {{{A[s]=A[c]}}}, so:


{{{(L/4)^2=C^2/(4*pi)}}}


{{{L^2/16=C^2/(4*pi)}}}


Multiply by {{{16pi}}}


{{{pi*L^2=4C^2}}}


Take the square root


{{{L*sqrt(pi)=2C}}}


But we know that {{{C=220-L}}}, so substitute:


{{{L*sqrt(pi)=2(220-L)}}}


Distribute and collect like terms:


{{{L*sqrt(pi)+2L=440}}}


Factor out L


{{{L(sqrt(pi)+2)=440}}}


And divide by {{{sqrt(pi)+2}}}


{{{green(L=440/(sqrt(pi)+2))}}}  inches


{{{C=220-L}}}, so


{{{C=220-(440/(sqrt(pi)+2))}}}


Simplify with LCD of {{{sqrt(pi)+2}}}


{{{C=(220(sqrt(pi)+2)-440)/(sqrt(pi)+2)}}}


{{{green(C=220*sqrt(pi)/(sqrt(pi)+2))}}} inches


Check your answer:


{{{A[s]=((440/(sqrt(pi)+2))/4)^2=110^2/(sqrt(pi)+2)^2}}}


{{{A[c]=pi*((220*sqrt(pi)/(sqrt(pi)+2))/(2*pi))^2=pi*(110/((sqrt(pi)+2)*sqrt(pi)))^2=(110^2)/(sqrt(pi)+2)^2}}}.  So the areas are equal


Now add the two lengths:  

{{{(220*sqrt(pi)/(sqrt(pi)+2))+(440/(sqrt(pi)+2))}}}


{{{(220*sqrt(pi)+440)/(sqrt(pi)+2)}}}


{{{(220(sqrt(pi)+2))/(sqrt(pi)+2)=220}}}, so the two lengths add to 220. 


Answer checks.


Final note:  the expressions for L and C developed above are the exact answers.  If you want to use a calculator to develop a decimal approximation of the answer, remember that you should never express an answer based on calculations involving measurements to greater precision than the least precise measurement given.  Since the length of the wire was expressed to the nearest inch, you should express your answer to the nearest inch as well.