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Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
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GMATinsight wrote:
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) \(4/ (√2-1)\)


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.)

\(? = x\)

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

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

The correct answer is therefore (C).


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

Regards,
Fabio.
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Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
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Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
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