GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 Jan 2020, 15:02

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.

Close

Request Expert Reply

Confirm Cancel

If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60727
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 02:44
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

77% (02:47) correct 23% (02:52) wrong based on 96 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
P
Joined: 21 Jun 2017
Posts: 399
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 02:52
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
VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1268
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]

Show Tags

New post 03 Nov 2019, 02:54
3
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
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1297
Location: India
Premium Member
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 03:00
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
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5748
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 03:50
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
Senior Manager
Senior Manager
User avatar
P
Joined: 12 Dec 2015
Posts: 474
Re: If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 09:27
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)
Rice (Jones) School Moderator
User avatar
P
Joined: 18 Jun 2018
Posts: 332
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28
GPA: 3.36
CAT Tests
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.  [#permalink]

Show Tags

New post 03 Nov 2019, 12:13
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
GMAT Club Bot
If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.   [#permalink] 03 Nov 2019, 12:13
Display posts from previous: Sort by

If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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