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

it is very confusing

Guest Jun 13, 2020

#1**0 **

Draw square(ABCD).

On the diagonal AC, find point E such that AE = 1.

Find point X on BC such that EX is perpendicular to CB.

Since AC is a diagonal of a square whose sides are each 1, the length of AC = sqrt(2).

Since AE = 1, EC = sqrt(2) - 1..

Triangle(ACB) is similar to triangle(ECX) [by AA].

This makes CE/CA = EX/AB

---> (sqrt(2) - 1) / sqrt(2) = EX / 1

---> (sqrt(2) - 1) / sqrt(2) = EX

---> EX = 0.293 (approximately)

[It would be the same istance to side CD.]

geno3141 Jun 13, 2020