BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

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

by GMATinsight » Thu Sep 20, 2018 9:38 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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) [m]4/ (2-√2)[/m]
B) [m]2√2/ (√2+1)[/m]
C) [m]4(√2-1)[/m]
D) [m]4(√2+1)[/m]
E) [m]4/ (√2-1)[/m]

www.GMATinsight.com
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

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

by fskilnik@GMATH » Fri Sep 21, 2018 8:27 am
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)

www.GMATinsight.com
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.)

Image
\[? = x\]
\[\left\{ \begin{gathered}
2L + x = 4 \hfill \\
x = L\sqrt 2 \,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,\sqrt 2 } \,\,\,\,2L = x\sqrt 2 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,x\sqrt 2 + x = 4\]
\[\,x\left( {\sqrt 2 + 1} \right) = \,\,4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = x = \frac{4}{{\sqrt 2 + 1}} = \frac{{4\left( {\sqrt 2 - 1} \right)}}{{\left( {\sqrt 2 + 1} \right)\left( {\sqrt 2 - 1} \right)}} = 4\left( {\sqrt 2 - 1} \right)\]

The correct answer is therefore [spoiler]__(C)______[/spoiler] .


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Sat Sep 22, 2018 8:08 pm
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) [m]4/ (2-√2)[/m]
B) [m]2√2/ (√2+1)[/m]
C) [m]4(√2-1)[/m]
D) [m]4(√2+1)[/m]
E) [m]4/ (√2-1)[/m]

www.GMATinsight.com
Refer to the image, which is self-explanatory.
Image

We see that 4 - 2x and √2x are the equal sides of the regular octagon.

Thus,

4 - 2x = √2x
16 - 16x + 4x^2 = 2x^2; squaring both the sides
8 - 8x + x^2 = 0

x = [8 ± √(64 - 32)] / 2 = = [8 ± √32] / 2 = [8 ± 4√2] / 2 = 4 ± 2√2

x cannot be 4 + 2√2 since x < 4, side of the square, thus x = 4 - 2√2

Thus, length of the octagon = 4 -2(4 - 2√2) = 4 - 8 + 4√2 = 4√2 - 4 = 4(√2 - 1)

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | London | Dubai | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1