Answer:
51.937515 feet.
Step-by-step 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.
[tex]100^{2} + 80^{2} = c^{2}[/tex]
10000 + 6400 = [tex]c^{2}[/tex]
16400 = [tex]c^{2}[/tex]
[tex]\sqrt{16400} = c[/tex]
128.062485 = c
180 - 128.062485 = 51.937515
She saves 51.937515 feet of distance by cutting across the gym.