Answer
The hose has a length of $50\sqrt 2$ ft.
Work Step by Step
When the diagonal divides a square into two triangles, we get two right triangles whose legs are congruent. If the legs are congruent, then the base angles are also congruent. So, essentially, we have a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, where the hypotenuse is $\sqrt 2$ times each leg.
We are given that each of the legs is $50$ feet long. Let's write an equation to solve for $x$, the length of the hose, which is the diagonal:
$x = \sqrt 2(50)$
Let's rewrite the radical in a more common form:
$x = 50\sqrt 2$
The hose has a length of $50\sqrt 2$ ft.
