#### Answer

The required length of the supporting wire is $c= 50\sqrt{2} ft$.

#### Work Step by Step

Using the Pythagorean theorem $c^2 = a^2 + b^2$, the length of the wire can be obtained by setting up an equation for the hypotenuse, $c$:
$a = 50ft$
$b = 50ft$
$c^2 = a^2 + b^2$
$c^2 = 50^2 + 50^2$
$c^2 = 50^2 + 50^2$
$c^2 = 5000$
$c= \sqrt{5000}$
$c= \sqrt{(2500·2)}$
$c= 50\sqrt{2} ft$