It is currently 29 Jun 2017, 09:44

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the area of triangular region RST is 25, what is the

Author Message
TAGS:

Hide Tags

Director
Joined: 05 Jan 2008
Posts: 688
If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

21 May 2008, 02:53
3
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:57) correct 44% (01:07) wrong based on 490 sessions

HideShow timer Statistics

If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is $$5\sqrt{2}$$.
(2) RST is a right isosceles triangle.
[Reveal] Spoiler: OA

_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

Last edited by Bunuel on 25 Oct 2013, 07:45, edited 1 time in total.
Edited the question and added the OA
Manager
Joined: 10 Mar 2008
Posts: 67

Show Tags

21 May 2008, 21:47
1
KUDOS
fresinha12 wrote:
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..

hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same
Attachments

tringle.JPG [ 36.1 KiB | Viewed 6106 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 39759

Show Tags

25 Oct 2013, 07:51
1
KUDOS
Expert's post
jlgdr wrote:
rohit929 wrote:
fresinha12 wrote:
If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is $$5\sqrt{2}$$.
(2) RST is a right isosceles triangle.

I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..

hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same

I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce
Let us know if this is the OA will you?
Thanks
Cheers
J

The correct answer is B. From (2) we know that 1/2*leg^2=25 --> we can get the length of the legs, and since it's a 45-45-90 right isosceles triangle, we can get the length of the hypotenuse too.
_________________
SVP
Joined: 12 Sep 2015
Posts: 1585
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

29 Sep 2016, 08:25
1
KUDOS
Top Contributor
prasannar wrote:
If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is $$5\sqrt{2}$$.
(2) RST is a right isosceles triangle.

VERY IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

This technique can save a lot of time.

Target question: What is the perimeter of RST?

Given: The area of triangular region RST is 25.

Statement 1: The length of one of the sides is 5√2
There are several possible triangles such that the length of one side is 5√2. Here are two:

Notice that the perimeter for each triangle is DIFFERENT. In other words, statement 1 does not lock our shape into having just one perimeter.
As such, statement 1 is NOT SUFFICIENT

Statement 2: The triangle is a right isosceles triangle
This fact alone forces the triangle into having a 90-degree angle, 2 equal angles and 2 equal sides. Of course there still many different triangles (with different perimeters) that meet these conditions:

HOWEVER, it is given that the area of the triangle is 25. Among the infinite number of isosceles right triangles, ONLY ONE has an area of 25.
So, statement 2 (along with the given information) "locks" our triangle into ONE and ONLY ONE shape, which means there's only one possible perimeter.
As such, statement 2 is SUFFICIENT.
IMPORTANT: Need we actually find the perimeter of this triangle? No. We need only recognize that we COULD find the perimeter (if we so inclined to do so)

[Reveal] Spoiler:
B

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

SVP
Joined: 04 May 2006
Posts: 1894
Schools: CBS, Kellogg

Show Tags

21 May 2008, 03:21
1
This post was
BOOKMARKED
prasannar wrote:
24. If the area of triangular region RST is 25, what is the perimeter of RST?
(1) The length of one side of RST is 5 sqrt 2.
(2) RST is a right isosceles triangle.

Plz explain

B

1/2*a^2 = 25 --> a =?
then b =a*sqare root(2)

and perimeter = b+ 2a, suff
_________________
VP
Joined: 18 May 2008
Posts: 1261

Show Tags

21 May 2008, 03:30
(1) The length of one side is given . but no information abt other sides. Insufficient
(2)The triangle is right isosceles let one side be x So area=1/2 *base*height=25.
here base=height (isoscels triagle)=x
Therefore, 1/2 *x*x=25 so x can be found
since right triangle so third side can be found say y
Perimeter is 2x+y
So sufficient
Intern
Joined: 07 May 2008
Posts: 19

Show Tags

21 May 2008, 03:47
The question stem tells us that 1/2 * b * h = 25 and asks us to determine what RS + ST + TR is.

(1) Statement just tells us what one of the 3 sides is where the b and h could still take several values and affect the other two sides:

Insufficient

(2) This statement simply tells us that b = h so b^2 = 50. If we know the lengths of two sides of a right triangle, then we can determine (I won't calculate it here since it would be a waste of time on test day) the length of the other. So:

Sufficient

_________________

Ryan S.
| GMAT Instructor |
Elite GMAT Preparation and Admissions Consulting
http://www.VeritasPrep.com

Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

21 May 2008, 06:47
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..
SVP
Joined: 28 Dec 2005
Posts: 1557

Show Tags

21 May 2008, 14:05
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

21 May 2008, 14:46
pmenon wrote:
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?

no it wont..just draw a 3-4-5 right angle tirangle or a 5-12-13 right angle,triangle..
SVP
Joined: 28 Dec 2005
Posts: 1557

Show Tags

21 May 2008, 15:28
but a 3-4-5 isnt an isoceles triangle ... or am i missing something ?
Manager
Joined: 21 Mar 2008
Posts: 81

Show Tags

21 May 2008, 15:39
fresinha12 wrote:
pmenon wrote:
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?

no it wont..just draw a 3-4-5 right angle tirangle or a 5-12-13 right angle,triangle..

Doesn't a right isosceles triangle means that the two equal sides make up the right angle?
Manager
Joined: 19 May 2008
Posts: 164
Location: Mumbai

Show Tags

21 May 2008, 20:31
the answer should be B since in a right isosceles triangle, base = height and area is (base*height)/2 - so we can get both the sides and then hypotenuse is side*sqrt 2 - so I am a bit surprised that the answer is C - it is anyway not A and D. E is also out of the question.
Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Show Tags

25 Oct 2013, 06:40
rohit929 wrote:
fresinha12 wrote:
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..

hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same

I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce
Let us know if this is the OA will you?
Thanks
Cheers
J
Senior Manager
Joined: 10 Mar 2013
Posts: 277
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

07 Dec 2013, 11:57
I don't understand why (1) is not sufficient. Doesn't (1) imply that the triangle is an isosceles right triangle since the height = 5*sqrt(2)?
Math Expert
Joined: 02 Sep 2009
Posts: 39759
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

08 Dec 2013, 07:03
TooLong150 wrote:
I don't understand why (1) is not sufficient. Doesn't (1) imply that the triangle is an isosceles right triangle since the height = 5*sqrt(2)?

No. Any triangle with the base (side) of $$5\sqrt{2}$$ and height of $$\frac{10}{\sqrt{2}}$$ would have the area of 25.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16036
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

09 Dec 2014, 15:42
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.
_________________
Intern
Joined: 21 Apr 2014
Posts: 40
If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

15 Feb 2015, 03:00
So the prompt tells us that the area of a triangle is 25 or that b*h=50
we are looking for the perimeter

(I) doesn't really tell us anything. Giving us one side is useless because we have no idea what the other sides could be
(II) actually tells us quite a lot. The fact that it is an isosceles right triangle tells us that b=h, so we know that those sides are rt(50) long and we can use that information to figure out the hypotenuse and add them up to get the perimeter.
_________________

Eliza
GMAT Tutor
bestgmatprepcourse.com

Intern
Joined: 17 Oct 2015
Posts: 1
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

19 Oct 2015, 11:55
B.
Statement 1- insufficient just says one side is 5 root 2 but no info about the other 2 sides is given
Statement 2- sufficient .. Isosceles right angled triangle therefore 1/2*side^2=25 side^2=50 side =root 50
Therefore hypotenuse = 2* (5 root 2) = 10
Perimeter =. 2(root 50) + 10
CEO
Joined: 17 Jul 2014
Posts: 2525
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If the area of triangular region RST is 25, what is the [#permalink]

Show Tags

28 Apr 2016, 18:46
prasannar wrote:
If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is $$5\sqrt{2}$$.
(2) RST is a right isosceles triangle.

from the given information: bh=50
we can have 5, 10, 5*sqrt(2)
or we can have 5*sqrt(2), 5*sqrt(2), 10
1 alone not sufficient.

2. we know that b=h => b^2=50 -> b=5*sqrt(2). since it is a 45-45-90 triangle, we can find the value of the hypotenuse.
2 alone is sufficient.

B
Re: If the area of triangular region RST is 25, what is the   [#permalink] 28 Apr 2016, 18:46
Similar topics Replies Last post
Similar
Topics:
Is the area of the triangular region above less than 20? 6 26 Jun 2017, 20:26
8 In the figure above, if the area of triangular region D is 4 6 30 Jun 2016, 06:46
14 What is the area of triangular region ABC above? 11 16 Nov 2016, 05:44
171 In the figure above, is the area of triangular region ABC 35 29 May 2017, 19:02
1 What is the area of rectangular region R? 4 10 Jan 2017, 03:49
Display posts from previous: Sort by