Question

Abcd is a square of side 4 inch. If each corner of square is cut identically so that resultant structure becomes regular eight sided polygon. What is length of side of octagon?

Answer 1

First of all, congratulations for the beautiful question. It´s exactly GMAT-like at its best: clearly written and easily-solved with proper understanding/tools!  

(All measures are in inches. Please follow image attached.)  

?=x?=x

{2L+x=4x=L2√⇒⋅2√2L=x2√⇒x2√+x=4{2L+x=4x=L2⇒⋅22L=x2⇒x2+x=4

x(2√+1)=4⇒?=x=42√+1=4(2√−1)(2√+1)(2√−1)=4(2√−1)x(2+1)=4⇒?=x=42+1=4(2−1)(2+1)(2−1)=4(2−1)

The correct answer is therefore (C).

This solution follows the notations and rationale taught in the GMATH method.  

Regards,  

Fabio.