Question 164142
<font size = 6 color = "red"><b>Edwin's solution:</font></b>

For what nonzero value of the radius is the circumference of a circle numerically equal to its area?
<pre><font size = 4 color = "indigo"><b>
{{{C=2pi*r}}}
{{{A=pi*r^2}}}

If we want {{{C=A}}}, then

{{{2pi*r=pi*r^2}}}

Divide both sides by {{{pi}}}:

{{{2pi*r/pi=pi*r^2/pi}}}

Cancel the {{{pi}}}'s

{{{2cross(pi)*r/cross(pi)=cross(pi)*r^2/cross(pi)}}}

{{{2r=r^2}}}

Get 0 on the right by adding {{{-r^2}}} to both sides:

{{{2r-r^2=0}}}

Factor out {{{r}}} on the left:

{{{r(2-r)=0}}}

Use the zero-factor property:

{{{matrix(3,3,      r=0, ",", 2-r=0 , "", "", -r=-2,  "", "", r=2   )}}}

Answer: the nonzero value of {{{r}}} is {{{r=2}}}.

Edwin</pre>