Alice and Amy are standing on the 2 opposite endpoints of the diagonal of a rectangle. (Well, this is the best way to think of the situation geometrically.)
The shortest distance is certainly when Amy walks straight through the diagonal. So, we need to find the length of the diagonal.
A diagonal divides a rectangle into 2 congruent (identical) right triangles. The sides of any of these 2 triangles are 100 ft and 60 ft, thus we can find the diagonal by the Pythagorean theorem:
[tex]|Diagonal|^2=100^2+60^2=10,000+3,600=13,600[/tex],
so,
[tex]|Diagonal|= \sqrt{16,600}\approx117 [/tex] (ft).
Answer: 117 ft
