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:

In the figure above an equilateral triangle with a perimeter [#permalink]

Show Tags

23 Feb 2005, 11:59

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (02:29) correct
0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

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

In the figure above an equilateral triangle with a perimeter of 18 inches is surrounded by a border inches thick. What is the area of the border?
(A) 18xsqrt(3)
(B) 21xsqrt(3)
(C) 24xsqrt(3)
(D) 27xsqrt(3)
(E) 36xsqrt(3)

Actually I have taken about ten and really have gotten no where. All I can figure out is that it is more than 18*sqrt3 because that is the summ of the four rectangle you make when you draw lines down from the edge of the inner triangle to the outer one...so that leave D or E...but in terms of how to calculate it I'm not quie sure...baneerjeas method seem legit....but just conceptually you can say that it must be a multiple of 9sqrt3 because that is the area of the inner triangle and since the outer and inner traiangle are equivalent their areas are related by ratio...therefore if you subtract the area of the outer triagle and inner triangle you should get a 9sqrt3 or a multiple ruling out B and C. So within two minutes I was able to get rid of A, B and C but not produce an answer.
_________________

Divide the area into 3 rectangles and 6 triangles.

Area of 3 rectangles = 3* 6*3^1/2 = 18*3^1/2

Area of 6 triangles = 6 * 1/2 *{(3^1/2)/tan 30} *3^1/2 = 9*3^1/2

Total = 27*3^1/2

Can't do anything under 2 mins while at work

can u plz explain how you solved the area of 6 triangles ? what is tan 30 ?

U already know the height which is 3^1/2.....also when u draw the triangles the top angle is divided in 30 each.....in trigonometry tan30 = height/base.....u need the base....and tan 30 = 1/3^1/2....so base = height/tan 30 = {3^1/2}^2 = 3

You don't have to memorize tan30, as long as you know that the side that is across from the 30 degree angel in a right triangle is half of the longest side (forgot what it is called in English). Then you can work out the other side. eg. a=sqrt(3), c=2sqrt(3). => b=3.

You don't have to memorize tan30, as long as you know that the side that is across from the 30 degree angel in a right triangle is half of the longest side (forgot what it is called in English). Then you can work out the other side. eg. a=sqrt(3), c=2sqrt(3). => b=3.

You don't have to memorize tan30, as long as you know that the side that is across from the 30 degree angel in a right triangle is half of the longest side (forgot what it is called in English). Then you can work out the other side. eg. a=sqrt(3), c=2sqrt(3). => b=3.

hm ? can u plz explain your equation ?

Quote:

(1/2*3*sqrt(3)*2+6*sqrt(3))*3=27sqrt(3)

My method really is the same with baner. It involves three steps. First is to divide the area into three parts, each part contains two side triangles and the rectangle in the middle. Second step is to figure out the length of the base of the little triangles using its heighth (sqrt(3)). Third, knowing the base and height of the two triangles, and the two sides for the rectangle, we can then calculate each respective area, and then add them up, and multiply by three.

You don't have to memorize tan30, as long as you know that the side that is across from the 30 degree angel in a right triangle is half of the longest side (forgot what it is called in English). Then you can work out the other side. eg. a=sqrt(3), c=2sqrt(3). => b=3.

hm ? can u plz explain your equation ?

Quote:

(1/2*3*sqrt(3)*2+6*sqrt(3))*3=27sqrt(3)

My method really is the same with baner. It involves three steps. First is to divide the area into three parts, each part contains two side triangles and the rectangle in the middle. Second step is to figure out the length of the base of the little triangles using its heighth (sqrt(3)). Third, knowing the base and height of the two triangles, and the two sides for the rectangle, we can then calculate each respective area, and then add them up, and multiply by three.

"Second step is to figure out the length of the base of the little triangles using its heighth (sqrt(3)). " Could u please explain this.... here we know height which is given (sqrt(3)) how did u get the base ? I just dont get it.

the angle subtended by the border thickness (sqrt of 3 ) at the vertex of the bigger triangle should be half of 60 deg = 30 deg.

So the extra half - length of the bigger trainge should be tan30 deg * sqrt 3 = 3. So the lenght of the bigger equialteral triangle will be 6+3+3 = 12.

You don't have to memorize tan30, as long as you know that the side that is across from the 30 degree angel in a right triangle is half of the longest side (forgot what it is called in English). Then you can work out the other side. eg. a=sqrt(3), c=2sqrt(3). => b=3.

hm ? can u plz explain your equation ?

Quote:

(1/2*3*sqrt(3)*2+6*sqrt(3))*3=27sqrt(3)

My method really is the same with baner. It involves three steps. First is to divide the area into three parts, each part contains two side triangles and the rectangle in the middle. Second step is to figure out the length of the base of the little triangles using its heighth (sqrt(3)). Third, knowing the base and height of the two triangles, and the two sides for the rectangle, we can then calculate each respective area, and then add them up, and multiply by three.