ABCD is a square of side 4 inch. If each corner of square is cut ident

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?

A)  4/ (2-√2) 
B)  2√2/ (√2+1) 
C)  4(√2-1) 
D)  4(√2+1) 
E)  4/ (√2-1)

Archit3110 · Answer

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?

A) 4/(2−√2)4/(2−√2)
B) 2√2/(√2+1)2√2/(√2+1)
C) 4(√2−1)4(√2−1)
D) 4(√2+1)4(√2+1)
E) 4/(√2−1)

GMATinsight  I am not able to solve the question completely, below are my two cents :

Given each side of square is 4, so and it is cut equally to an octagon so lets assume it to be cut equally on each by x so now each side of the square will be ( 4-2x) , perimeter of the square shape with 8 points will be (4-2x) * 4: (16-8x) and we can deduce that each side of the octagon would be (16-8x)*1/8 : (2-x).

Each side of the octagon would be (2-x).

I am not able to solve further than this..not even sure whether my aforementioned approach is correct or not....

GMATinsight · Answer

Refer the figure attached for how the octagon will be obtained by chopping of fthe corners identically Here Side of square, S = 4 and Side of Octagon, a = ? Now, we see that each corner cut off is a right triangle with sides a√2 as hypotenuse of the triangle being a i.e. \frac{a}{√2}+a+\frac{a}{√2} = 4 i.e. a+\frac{2a}{√2} = a+a√2 = 4 i.e. a = 4/(√2+1) = 4(√2-1) Answer: Option C Hope this helps!!!

fskilnik · Answer

Hi GMATinsight!

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

\left\{ \begin{gathered}
 2L + x = 4 \hfill \
 x = L\sqrt 2 \,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,\sqrt 2 } \,\,\,\,2L = x\sqrt 2 \hfill \ 
\end{gathered} ight.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,x\sqrt 2 + x = 4

\,x\left( {\sqrt 2 + 1} ight) = \,\,4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = x = \frac{4}{{\sqrt 2 + 1}} = \frac{{4\left( {\sqrt 2 - 1} ight)}}{{\left( {\sqrt 2 + 1} ight)\left( {\sqrt 2 - 1} ight)}} = 4\left( {\sqrt 2 - 1} ight)

The correct answer is therefore (C).

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

Regards, 
Fabio.

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ABCD is a square of side 4 inch. If each corner of square is cut ident

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ABCD is a square of side 4 inch. If each corner of square is cut ident

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