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 500,000 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:

Isosceles right triangle with perimeter 16+16(2^0.5). What [#permalink]

Show Tags

19 Oct 2006, 23:30

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Isosceles right triangle with perimeter 16+16(2^0.5). What is the length of the hypothenuse?

I know this is a special triangle and therefore the sides are in a ratio of 1:1:2^0.5 but I am having a hard time setting this up. The official answer is 16...how do you get there?

Isosceles right triangle with perimeter 16+16(2^0.5). What is the length of the hypothenuse?

I know this is a special triangle and therefore the sides are in a ratio of 1:1:2^0.5 but I am having a hard time setting this up. The official answer is 16...how do you get there?

Thak you very much,

Primeminister

You must remember that the sum of two sides of the triangle cannot be larger than the length of one of the sides....

Therefore, if the perimeter of isoscles triangle is 16+16(2^0.5)... hypotenuse must be equal 16, because the other two sides are equal in legth and the sum of those two sides must be larger than the remaining side....

Thanks SimaQ...i follow the triangle logic of what you said...not sure how that makes the hypothenuse 16 just by looking at the 16+16(2^0.5)??? Perhaps you can set it up in an equation so I can see it.

I can do the following:
x+x+x(2^0.5)=16+16(2^0.5) Solving for x is very easy if you have a calculator and it gets the right answer. A bit tougher doing it just with a pencil.

Perimeter: 16+16(2^0.5).....
From stem we know that the two sides are eqaul....
From the rule above we know that those two sides cannot be equall to 8+8=16, because the remaining side, that is hypotenuse, would be equal to more than 16, that is 16(2^0.5)....

Therefore the sum of the other two sides must be equal to 16(2^0.5)
And the remaining side, hypotenuse, 16....

Just multiply sqrt(2) to your special triangle:
1:1:sqrt(2)
You get
sqrt(2):sqrt(2):2
which gives you perimeter 2+2sqrt(2)
Now you know the ratio is 2:2+2aqrt(2) or 16:16+16sqrt(2).
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.