Last visit was: 12 Sep 2024, 16:51 It is currently 12 Sep 2024, 16:51
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6065
Own Kudos [?]: 14128 [12]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 8060
Own Kudos [?]: 4324 [1]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6065
Own Kudos [?]: 14128 [3]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 891
Own Kudos [?]: 1447 [0]
Given Kudos: 56
Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
GMATinsight
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!

$$? = x$$

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

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

The correct answer is therefore (C).

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

Regards,
Fabio.
Attachments

21Set18_4q.gif [ 5.65 KiB | Viewed 3295 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 34824
Own Kudos [?]: 878 [0]
Given Kudos: 0
Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: ABCD is a square of side 4 inch. If each corner of square is cut ident [#permalink]
Moderator:
Math Expert
95478 posts