A Right triangle is a triangle that has an angle whose measure is 90 degrees.
A 45°-45°-90°-degree triangle is a Right triangle that has two angles that measure 45 degrees. This triangle has two sides of equal length.
You can identify that the triangle given in the exercise is a 45°-45°-90°-degree triangle.
According to the 45°-45°-90° Triangle theorem:
[tex]hypotenuse=\sqrt[]{2}\cdot leg[/tex]
In this case:
[tex]\begin{gathered} hypotenuse=x \\ leg=100ft \end{gathered}[/tex]
Substituting values into the equation and evaluating, you get that length of the path will be the following:
[tex]\begin{gathered} x=(\sqrt[]{2})(100ft) \\ x=100\sqrt[]{2}ft \\ x\approx141.42ft \end{gathered}[/tex]
The answer is:
[tex]x\approx141.42ft[/tex]
