GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 23 Apr 2021, 09:02
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

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
Your Progress

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.
9 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 74510
CAT Tests Top Member of the Month
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 01:44
27
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

71% (02:48) correct 29% (02:56) wrong based on 298 sessions

Hide Show timer Statistics

If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\)

E. \(2x + \sqrt{2}\)


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Most Helpful Community Reply
avatar
V
Dillesh4096
VP
VP
Joined: 20 Jul 2017
Posts: 1499
Location: India
Concentration: Entrepreneurship, Marketing
WE:Education (Education)
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 01:54
7
Kudos
5
Bookmarks
Bunuel wrote:
If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\)

E. \(2x + \sqrt{2}\)


Are You Up For the Challenge: 700 Level Questions


The sides of an isosceles right angled triangle will be a, a, \(\sqrt{2}\)a
Perimeter = a + a + \(\sqrt{2}\)a = (2 + \(\sqrt{2}\))a

Area = \(\frac{1}{2}*a*a\) = \(\frac{a^2}{2}\)

Given Area = \(2x^2 + 2x + \frac{1}{2}\)
--> \(\frac{a^2}{2}\) = \(2x^2 + 2x + \frac{1}{2}\)
--> \(a^2 = 4x^2 + 4x + 1\)
--> \(a^2 = (2x + 1)^2\)
--> \(a = 2x + 1\)

Required Perimeter = (2 + \(\sqrt{2}\))a = \((2 + \sqrt{2})(2x + 1)\)

IMO Option D
General Discussion
User avatar
V
ShankSouljaBoi
Director
Director
Joined: 21 Jun 2017
Posts: 816
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D), IIMA PGPX'22 (D), Desautels '23 (D), Schulich Sept '23 (D), WBS (D)
GMAT 1: 620 Q47 V30
GMAT 2: 650 Q48 V31
GMAT 3: 660 Q49 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Reviews Badge CAT Tests
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 01:52
1
Kudos
D let sides b y , y and sqrty
Then
(Y^2)/2= 2x^2+2X+ 1/2
Y= 2x+1
Y + y + sqrt(y) = perimeter = D

Posted from my mobile device
_________________
If GMAT is Nasha , I am the BhamBhole
Signature Read More
User avatar
V
nick1816
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 2265
Location: India
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 02:00
1
Kudos
Assume equal sides of right angled isosceles triangle= y
hypotenuse= \(\sqrt{2}y\)
Perimeter= y+y+\(\sqrt{2}y\)= \((2+\sqrt{2})y\)
Area of such triangle is \(\frac{1}{2}*y^2\)......(1)


\(2x^2 + 2x + \frac{1}{2}\)
=\(\frac{1}{2}\)* \(4x^2 + 4x + 1\)

=\(\frac{1}{2}\)* \((2x+ 1)^2\)......(2)

Comparing (1) and (2)

y=2x+1

Perimeter of triangle = \((2+\sqrt{2})(2x+1)\)



Bunuel wrote:
If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\)

E. \(2x + \sqrt{2}\)


Are You Up For the Challenge: 700 Level Questions
User avatar
V
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 6967
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 02:50
isosceled ∆ right angled ; sides x:x:x√2
for area
1/2 * a^2 = \(2x^2 + 2x + \frac{1}{2}\).

a=2x+1
the perimeter of side = 4x+2+√2.2x+√2
IMO D \((2 + \sqrt{2})(2x + 1)\)

Bunuel wrote:
If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\)

E. \(2x + \sqrt{2}\)


Are You Up For the Challenge: 700 Level Questions
User avatar
V
hiranmay
Director
Director
Joined: 12 Dec 2015
Posts: 680
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 08:27
If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\) --> correct

E. \(2x + \sqrt{2}\)

Solution:
length of the each two equal side = a
So area = a*a/2 = \(2x^2 + 2x + \frac{1}{2}\)
=> a^2=4x^2+4x+1=(2x+1)^2
=> a = 2x+1
So perimeter of the right angled isosceles triangle = a+a+ a \(\sqrt{2}\) = a (2+\(\sqrt{2}\) ) = (2+\(\sqrt{2}\) )*(2x+1)
User avatar
P
bebs
Current Student
Joined: 18 Jun 2018
Posts: 352
Concentration: Finance, Healthcare
Schools: Jones '22 (M$), McCombs '22 (WL), Kelley '22 (A$)
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  03 Nov 2019, 11:13
The area, A of a right angled isosceles triangle is \(\frac{1}{2}\)\(i^{2}\), where i represents the equal legs

Also, the sides of a right angled isosceles triangle are i, i, i\(\sqrt{2}\)

Therefore, \(\frac{1}{2}\)\(i^{2}\) = 2\(x^{2}\)+2x+\(\frac{1}{2}\) ==> \(i^{2}\) = 4\(x^{2}\)+4x+1 ==> i = 2x + 1 (since the sides are positive)

Therefore, perimeter = 2x + 1 + 2x + 1 + \(\sqrt{2}\)(2x+1) ==> (2x +1)(2+\(\sqrt{2}\)) ==> the answer is D
avatar
S
NischalP
Current Student
Joined: 26 Nov 2019
Posts: 74
Concentration: Technology, Strategy
Schools: Schulich(Jan) '22 (A)
GMAT 1: 650 Q48 V31
Reviews Badge
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  22 Apr 2020, 07:10
Assume X=1
Area of the triangle would be 9/2

let a be the side and h of the isoceles right triangle
a^2/2=9/2 , a=3
Perimeter will be a+a+sqrt(a) [Sides for isoceles triangle] = 6 + 3sqrt(2)
Substitute x=1 in the answer options and
IMO D would match the answer.

Simpler way and could be done in a minute.
_________________
GMAT 2nd Attempt In Progress..

Negate till you are positive about the choice
Signature Read More
User avatar
V
zhanbo
Director
Director
Joined: 27 Feb 2017
Posts: 697
Location: United States (WA)
GMAT 1: 760 Q50 V42
GRE 1: Q169 V168
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink] New post  22 Mar 2021, 12:59
hiranmay wrote:
If a right angled isosceles triangle has an area of \(2x^2 + 2x + \frac{1}{2}\). What is its perimeter?


A. \(3(x + 1)\)

B. \(\sqrt{2}(x^2 + 1)\)

C. \((\sqrt{2}x - 1)(2x + 1)\)

D. \((2 + \sqrt{2})(2x + 1)\) --> correct

E. \(2x + \sqrt{2}\)

Solution:
length of the each two equal side = a
So area = a*a/2 = \(2x^2 + 2x + \frac{1}{2}\)
=> a^2=4x^2+4x+1=(2x+1)^2
=> a = 2x+1
So perimeter of the right angled isosceles triangle = a+a+ a \(\sqrt{2}\) = a (2+\(\sqrt{2}\) ) = (2+\(\sqrt{2}\) )*(2x+1)


Because x can be negative such as -2,
With a^2=4x^2+4x+1=(2x+1)^2
We should get: a = |2x+1|

There is no such option in answers though.
GMAT Club Bot
gmatclubot
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. [#permalink]
22 Mar 2021, 12:59
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9755 posts
Bunuel
Math Expert
74510 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2445 posts
generis
Senior SC Moderator
4690 posts
Feedback

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions