In triangle ABC, angle ABC is 90 degrees. What the perimeter : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 03:36

### 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

# In triangle ABC, angle ABC is 90 degrees. What the perimeter

Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 11

Kudos [?]: 850 [0], given: 4

In triangle ABC, angle ABC is 90 degrees. What the perimeter [#permalink]

### Show Tags

26 Dec 2007, 10:49
In triangle ABC, angle ABC is 90 degrees.
What the perimeter of triangle ABC?

1. AB + BC = 7
2. AB/BC = 3/4

Can someone tell me why statement 1 is insuff. if we shift the values between AB and BC, the total of these two sides will still be 7. how does it affect the perimeter?
Director
Joined: 08 Jun 2007
Posts: 583
Followers: 2

Kudos [?]: 97 [1] , given: 0

Re: perimeter of a triangle [#permalink]

### Show Tags

26 Dec 2007, 11:26
1
KUDOS
bmwhype2 wrote:
In triangle ABC, angle ABC is 90 degrees.
What the perimeter of triangle ABC?

1. AB + BC = 7
2. AB/BC = 3/4

Can someone tell me why statement 1 is insuff. if we shift the values between AB and BC, the total of these two sides will still be 7. how does it affect the perimeter?

if you shift values , total will remain same but the hypotenuse will change which affects the perimeter.

C.
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 544

Kudos [?]: 3545 [0], given: 360

### Show Tags

26 Dec 2007, 10:56
1)

P= AB + BC + AC = (AB + BC) + √(AB² + BC²) = 7 + √(AB² + (7-AB)²) =
=7+√(AB² + (7-AB)²) = 7+√(2AB² - 14AB +49)

2AB² - 14AB +49 is not constant.
Director
Joined: 12 Jul 2007
Posts: 862
Followers: 15

Kudos [?]: 285 [0], given: 0

### Show Tags

26 Dec 2007, 10:58
A^2+B^2=C^2 for the sides of a right triangle with the legs being A and B and the hypotenuse being C.

1. tells us the two legs add up to 7.

3^3+4^2=25 so the legs are 3-4-5 for a perimeter of 12

BUT they could also be 5 and 2 since 5+2 = 7 (or they could be 6 and 1)

2^2+5^2=29 so the legs would be 2-5-sqrt(29) for a different perimeter altogether.

2. AB/BC tells us the ratio of the two legs is 3/4. This is insufficient on it's own as the legs could be 3-4, 9-12, 30-40...any two numbers in the 3/4 ratio.

HOWEVER, when taken together...we know the ratio between the two legs is 3/4 and they must add up to 7. This means the only possible values for the legs are 3 and 4. Giving the entire perimeter 3+4+5 or 12

Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 193
WE 1: SAP consultant-IT 2 years
WE 2: Entrepreneur-family business 2 years
Followers: 5

Kudos [?]: 13 [0], given: 12

Re: perimeter of a triangle [#permalink]

### Show Tags

15 Jun 2011, 00:04
this question might seem lame, but I am missing a concept,

ab+bc = 7 and abc = 90 degree, does this not imply we have a 3-4-5 triangle here ?

are other values of ab and bc are possible with abc = 90 degree ?
_________________

Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1701 [0], given: 376

Re: perimeter of a triangle [#permalink]

### Show Tags

20 Jun 2011, 01:34
bblast wrote:
this question might seem lame, but I am missing a concept,

ab+bc = 7 and abc = 90 degree, does this not imply we have a 3-4-5 triangle here ?

are other values of ab and bc are possible with abc = 90 degree ?

does this not imply we have a 3-4-5 triangle here ?
No, it doesn't imply so. That is just one of the infinite possibilities.

ab=1, bc=6, ac= $$\sqrt{1^2+6^2}=\sqrt{37}$$
ab=2.11, bc=4.89, ac= $$\sqrt{(2.11)^2+(4.89)^2}$$
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7118
Location: Pune, India
Followers: 2128

Kudos [?]: 13618 [0], given: 222

Re: perimeter of a triangle [#permalink]

### Show Tags

21 Jun 2011, 02:25
Let me point out here that Pythagorean triplets (3,4,5 etc) give you the sides of a right angled triangle such that each side is an integer. But the sides of a right angled triangle needn't necessarily be integers.
If it is given that hypotenuse is 5, the sides could be 3,4 or they could be 1, $$\sqrt{24}$$ or 2, $$\sqrt{21}$$ etc...
Similarly, if sum of the legs is 7, the sides could be 3,4 or 1,6 or 2,5 etc... For each of these, the hypotenuse will be different.

What helps in visualizing whether there are multiple solutions is drawing. Make a hypotenuse of length 5 cm. As you keep changing the incline of the hypotenuse, you keep getting different values for the other two sides.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: perimeter of a triangle   [#permalink] 21 Jun 2011, 02:25
Similar topics Replies Last post
Similar
Topics:
1 30-60-90 Triangle Property Question 4 14 Apr 2013, 10:57
1 Condition for a right angle triangle 3 03 Mar 2013, 23:13
1 Right angled triangle in a circle 3 07 Feb 2012, 12:09
30 60 90 triangle 1 14 Aug 2010, 17:48
3 In the diagram to the right, triangle ABC has a right angle 17 03 Jul 2008, 15:12
Display posts from previous: Sort by