Answer
$50 \sqrt{2}\; feet$.
Work Step by Step
Let the width of the pond be $x$.
In the figure we have a right angle triangle with two equal legs $50\; feet$
and hypotenuse $=x$.
Use the Pythagorean theorem.
$\Rightarrow x^2=50^2+50^2$
Simplify.
$\Rightarrow x^2=2500+2500$
$\Rightarrow x^2=5000$
Apply the Square Root Property.
$\Rightarrow x=+\sqrt{5000}$ or $x=-\sqrt{5000}$.
We take positive value because the hypotenuse has a positive length.
$\Rightarrow x=+\sqrt{5000}$
Factor the right hand side.
$\Rightarrow x=+\sqrt{5^2\cdot 10^2\cdot 2}$
Simplify.
$\Rightarrow x=5\cdot 10 \sqrt{2}$
$\Rightarrow x=50 \sqrt{2}$
Hence, the width of the pond is $50 \sqrt{2}\; feet$.
