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 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 

 Jun 13, 2020
 #1
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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.]  

 Jun 13, 2020
 #2
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but what is the shortest distance from e to the side?

Guest Jun 14, 2020

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