Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 348: 49

$2236.07$ feet

Let's note the length of the guy's wire by $x$. Then, by the Pythagorean Theorem, we have: $$\begin{aligned} x^2&= 1000^2+2000^2\\ &=5000000\\ x&= \pm\sqrt{5000000}\\ x&=\sqrt{5000000}\\ x& \approx 2236.07 \end{aligned}$$ We took only the positive value, since the length of the wire must be positive. The required length of the wire is about $2236.07$ feet.