Answer:
51.937515 feet.
Explanation:
If she goes across the perimeter, it will be 100 + 80 = 180 feet.
Use pythagoras' theorem to find out the distance of cutting across the gym.
10000 + 6400 =
16400 =
128.062485 = c
180 - 128.062485 = 51.937515
She saves 51.937515 feet of distance by cutting across the gym.