Question 156612
i think i got it.
area of a circle = {{{ pi * r^2}}}.
area of square is {{{s^2}}}.
so {{{s^2 = pi * r^2}}} is a requirement.
if {{{s^2 = pi * r^2}}}, then {{{s = sqrt (pi * r^2)}}} = {{{r * sqrt (pi)}}}.
circumference of a circle is {{{2*pi*r}}}.
perimeter of a square is {{{4*s}}}.
circumference of the circle plus the perimeter of the square must equal 350mm, so the second formula required is {{{(2*pi*r) + (4*s) = 350}}} mm. 
from the first formula we determined that {{{s = r * sqrt (pi)}}}.
substituting for s in the second equation to eliminate one unknown we get {{{ (2*pi*r) + (4 * r * sqrt (pi)) = 350}}} mm.
factoring out the r we get {{{r * ((2 * pi) + (4 * sqrt (pi) )) = 350 }}} mm.
solving for r, we get {{{ r = 350 / ((2 * pi) + (4 * sqrt (pi) )) }}}.
after doing the calculations, r becomes 26.1721365.
{{{2*pi*r}}} becomes 164.4443835.
{{{4*s}}} becomes 350 - 164.4443835 becomes 185.5556165.
s becomes 46.38890413.
{{{pi * r^2}}} becomes 2151.930426
{{{s^2}}} becomes 2151.930426
area of square equals area of circle.
perimeter of circle plus perimeter of square = 350 mm.