Answer
The length of the bent wire is closest to 7.
Work Step by Step
Take the sum of all the sides.
$\sqrt {20} + \sqrt {8}$
Approximate the square roots based on the nearest perfect squares.
$\sqrt {20}\approx4.4$
because it is between $\sqrt {16}$ and $\sqrt {25}$ (between 4 and 5).
$\sqrt {8}\approx2.9$
because it is between $\sqrt{4}$ and $\sqrt {9}$ (between 2 and 3).
so...
$\sqrt {20} + \sqrt {8}\approx4.4+2.9\approx7$.
