Euclidian vs. Manhattan

Geometry Level 3

Alice and Beth are playing in a rectangular field. Alice bets Beth that she can beat Beth in a race from one corner of the field to the other. Alice is so confident that she'll win that she says she can still win if Beth races straight to the other point and Alice races along the perimeter.

The race results in a tie: Alice and Beth reach the other corner at the exact same time. If Beth ran 50 metres, Alice ran \(A\) metres. What is possible interval of \(A\)?


Inspired by some kids I saw doing this.
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