Answer
The shorter path is 125 yd.
Work Step by Step
Use the Pythagorean theorem to find the length of each path.
$75^2+100^2=c^2 \longrightarrow$ find the squares
$5625+10000=c^2 \longrightarrow$ add
$15625=c^2 \longrightarrow$ find the square root of each side
$\sqrt {15625}=\sqrt {c^2} \longrightarrow$ simplify
$125=c$
$50^2+240^2=c^2 \longrightarrow$ find the squares
$2500+57600=c^2 \longrightarrow$ add
$60100=c^2 \longrightarrow$ find the square root of each side
$\sqrt {60100}=\sqrt {c^2} \longrightarrow$ simplify
$245.2=c$
