Answer
The length of the circle is $\approx169.1$
The length of the square is $\approx190.9$
Work Step by Step
Let's say that the part of wire used to form circle is $x$, then the second part used for square will be $y$ ($x+y=360$). Let $a$ be side of the square and $r$ radius of the circle.
Area of circle is: $\pi r^2$
Area of square is: $a^2$
According to the problem, we know that the areas equal to each other.
$a^2=\pi r^2$
$a=\sqrt{\pi r^2}$ (We don't consider negative option, since the length cannot be a negative number)
$x=2\pi r$
$y=4a$
$4a+2\pi r = 360$
$4\sqrt{\pi r^2} + 2\pi r = 360$
$4r\sqrt\pi+2\pi r = 360$
$r(2\sqrt\pi+\pi) = 180$
$r=\frac{180}{2\sqrt\pi+\pi}\approx26.9199$
$r\approx26.92$
Circle length = $2\pi \times 26.92 \approx 169.1$
Square length = $360-169.1=190.9$
