Darden is releasing R3 decisions: Check your profile status | EXPECTING SOON - Stanford and Fuqua | Join Chat Room for Live Updates

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: right Triangle Theorem [#permalink]
15 Jul 2012, 22:24

Expert's post

alphabeta1234 wrote:

I want to understand right triangles a little better.

So if you have a Triangle and the given facts are:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10

Can we conclude the triangle is a 6-8-10 ( a variant of the 3-4-5) triangle? If not, can we calculate the permiter of the triangle?

How about the introduction of a new fact:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10 3) All the sides of the triangle are integer values.

Now can we concludes it is a 6-8-10 triangle?

With the exception of having a 90* degree angle, what conditions do we need to ensure a triangle is a Pythagorean triangle?

There are various ways in which you can have a right triangle with hypotenuse 10. The sides could be 1, \(\sqrt{99}\), 10 or \(\sqrt{2}\), \(\sqrt{98}\), 10 or 6, 8, 10 etc

If sides are integral, it does add constraint to the values that the sides can take. Pythagorean triplets give sides of right triangles that have all integral sides. But that doesn't ensure that the hypotenuse will imply a single value for the other two sides in all cases (but it does in most). If hypotenuse is 10, the sides will be 6 and 8 but if the hypotenuse is 65, the other two sides could be (16, 63) or (33, 56)

Re: right Triangle Theorem [#permalink]
16 Jul 2012, 15:45

Hey Karishma,

What about

How about the introduction of a new fact:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10 3) All the sides of the triangle are integer values.

Does the third condition gaurentee that we have a unique triplet triangle? Because as you mentioned we can have a right triangle with hypotunse of 10 with three possible side orders:

But notice only one of choices has all of its sides as integer values!! (1) and (2) do not have integer values as sides.

Can I therefore state the condition :

IF the triangle is: 1) A right triangle 2) One of the sides is triplet value (3,4,5) (6,8,10) (5,12,13) (8,15,17) etc 3) All of the sides are integer value

Re: right Triangle Theorem [#permalink]
16 Jul 2012, 22:30

Expert's post

alphabeta1234 wrote:

Hey Karishma,

What about

How about the introduction of a new fact:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10 3) All the sides of the triangle are integer values.

Does the third condition gaurentee that we have a unique triplet triangle? Because as you mentioned we can have a right triangle with hypotunse of 10 with three possible side orders: (actually, there are innumerable ways in which you can have the hypotenuse 10. I just gave 3 examples. But yes, only one of them has all integral sides)

But notice only one of choices has all of its sides as integer values!! (1) and (2) do not have integer values as sides.

Can I therefore state the condition :

IF the triangle is: 1) A right triangle 2) One of the sides is triplet value (3,4,5) (6,8,10) (5,12,13) (8,15,17) etc 3) All of the sides are integer value

Then the triangle is a triplet and unique?

Read the above post again: "If sides are integral, it does add constraint to the values that the sides can take. Pythagorean triplets give sides of right triangles that have all integral sides. But that doesn't ensure that the hypotenuse will imply a single value for the other two sides in all cases (but it does in most). If hypotenuse is 10, the sides will be 6 and 8 but if the hypotenuse is 65, the other two sides could be (16, 63) or (33, 56)"

Let me re-phrase it:

If hypotenuse is 10, the sides must be 6, 8, 10 - unique If hypotenuse is 65, the sides are not unique. There are two pythagorean triplets with hypotenuse 65. They are (16, 63, 65) and (33, 56, 65).

Often, with a given hypotenuse, only one pythagorean triplet is formed, but it is not necessary. _________________

Re: right Triangle Theorem [#permalink]
17 Jul 2012, 18:08

VeritasPrepKarishma wrote:

There are various ways in which you can have a right triangle with hypotenuse 10. The sides could be 1, \(\sqrt{99}\), 10 or \(\sqrt{2}\), \(\sqrt{98}\), 10 or 6, 8, 10 etc

More than various, there is actually an infinite amount of right triangles with hypotenuse = 10!!

Re: right Triangle Theorem [#permalink]
19 Jul 2012, 01:11

Given facts are:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10

Q. Can we conclude the triangle is a 6-8-10 ( a variant of the 3-4-5) triangle? A. No you CANNOT conclude that its a 6-8-10 triangle as you have only the following things known:-- Suppose base is b height is d and hypotenous is h then what you know is h=10 and a^2 + b^2 = h^2 = 10^2 So there can be any number of values for a and b! So you CANNOT conclude that it is a 6-8-10 traingel

Q. If not, can we calculate the permiter of the triangle? A. NO you cannot find the perimeter of teh trainagle as you don't know the individual sides of the traingle/(as explained above)

How about the introduction of a new fact:

1) Right triangle (so one side is 90*) 2) The hypotunse is equal to 10 3) All the sides of the triangle are integer values.

Q. Now can we concludes it is a 6-8-10 triangle? A. Suppose base is b height is d and hypotenous is h then what you know is h=10 and a^2 + b^2 = h^2 = 10^2 Since a and b can only be positive integers so, a can be 6 or 8 and b can be 8 0r 6 respectively. YES you can conclude that it is a 6-8-10 triangle

Q. With the exception of having a 90* degree angle, what conditions do we need to ensure a triangle is a Pythagorean triangle? A. Pythagorean Triangle. I doubt if there is a term like that! But i know what you mean. You mean what all do we need to apply Pythagorean Theorm. Pythagorean Theorm is defined only for right angled triangles. Any triangle which is a right angled triangle => You can use Pythagorean Theorm. Any triangle which is NOT a right andled triangle => You CANNOT use Pythagorean Theorm.

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...

I started running back in 2005. I finally conquered what seemed impossible. Not sure when I would be able to do full marathon, but this will do for now...