Question

Square ABCD has a side length of 1. Point E lies on the interior of ABCD, and is on

the line AC such that the length of AE is 1. Find the shortest distance from point E
to a side of square ABCD.

Answer 1

1 -(√2)/2 ≈ 0.292893

Explanation:

The diagonal length AC is √2, so the distance EC is √2 -1. That is the diagonal of the square whose side length is the length of interest. That side length will be (√2)/2 times the length of EC.

shortest distance from E = (√2 -1)(√2)/2 = 1 -(√2)/2