Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register
 

Can anyone help me figure this one out?

This topic has 2 expert replies and 2 member replies
Bookmark
Previous Topic Next Topic
debonairdrz Just gettin' started! Default Avatar
Joined
25 Apr 2012
Posted:
1 messages
Can anyone help me figure this one out? Post Wed Apr 25, 2012 1:01 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
    what is the length of one side of the triangle in meters?

    (A)6
    (B)8
    (C)4 sqrt(2)
    (D)2 sqrt(3)
    (E)4 sqrt(3)


    I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


    I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

    x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

    3x=(1/2)xh

    Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

    Therefore I now have:

    3x=(1/2)x sqrt(3)(x/2)


    That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

    Any and all help is greatly appreciated.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Mr Smith Just gettin' started! Default Avatar
    Joined
    06 Apr 2012
    Posted:
    18 messages
    Followed by:
    1 members
    Thanked:
    5 times
    GMAT Score:
    770
    Post Wed Apr 25, 2012 1:28 pm
    hey debonairdrz,

    U have got it right till the equation.
    U are doing something wrong while simplyfying it.

    3x = sqrt(3)*(x^2)/4
    Thus x/4 = 3/sqrt(3)
    Thus x = 4*sqrt(3)

    Note: I am following the same nomenclature as you are n the solution. as in x is the side of the triangle Smile

    _________________
    Kindly Use Thanks Button as liberally as you receive replies. Smile

    Mr. Smith

    Thanked by: debonairdrz

    GMAT/MBA Expert

    Stuart Kovinsky GMAT Instructor
    Joined
    08 Jan 2008
    Posted:
    3156 messages
    Followed by:
    461 members
    Thanked:
    1433 times
    GMAT Score:
    800
    Post Wed Apr 25, 2012 8:42 pm
    Mr Smith wrote:
    hey debonairdrz,

    U have got it right till the equation.
    U are doing something wrong while simplyfying it.

    3x = sqrt(3)*(x^2)/4
    Thus x/4 = 3/sqrt(3)
    Thus x = 4*sqrt(3)

    Note: I am following the same nomenclature as you are n the solution. as in x is the side of the triangle Smile
    Perfect solution, just to clarify a few steps:

    3x = sqrt(3)*(x^2)/4

    We know that x is positive (since it's the side of a triangle), so we can safely divide both sides by x to get:

    3 = sqrt3 * x/4

    Multiplying both sides by 4:

    12 = sqrt 3 * x

    Dividing both sides by sqrt3:

    12/sqrt3 = x

    It's mathematically inelegant to leave a root in the denominator of a fraction, so we "rationalize the denominator" by multiplying the fraction by (root we want to get rid of / root we want to get rid of). Accordingly:

    12*sqrt3/sqrt3*sqrt3 = x
    12(sqrt3)/3 = x
    4(sqrt3) = x

    _________________
    Stuart Kovinsky, B.A. LL.B.
    Kaplan Test Prep & Admissions
    Toronto Office
    1-800-KAP-TEST
    www.kaptest.com

    Learn more about me

    Thanked by: debonairdrz
    Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
    nisagl750 Really wants to Beat The GMAT!
    Joined
    31 Jan 2012
    Posted:
    145 messages
    Followed by:
    2 members
    Thanked:
    16 times
    Post Thu Apr 26, 2012 1:20 am
    debonairdrz wrote:
    If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
    what is the length of one side of the triangle in meters?

    (A)6
    (B)8
    (C)4 sqrt(2)
    (D)2 sqrt(3)
    (E)4 sqrt(3)


    I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


    I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

    x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

    3x=(1/2)xh

    Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

    Therefore I now have:

    3x=(1/2)x sqrt(3)(x/2)


    That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

    Any and all help is greatly appreciated.
    I guess your equation read like:
    3x = (1/2)x*sqrt(3)(x/2)
    Simplifying it we get
    3x = sqrt(3)/4*x^2

    Solving this we get x=12/sqrt(3)

    Hope you got this answer.
    Now all you hacve to do is rationalise it.

    i.e. multiply and divide it by sqrt(3)
    So you'll get X=4*sqrt(3)

    Hope it helps Wink

    Thanked by: debonairdrz

    GMAT/MBA Expert

    GMATGuruNY GMAT Instructor
    Joined
    25 May 2010
    Posted:
    6093 messages
    Followed by:
    1039 members
    Thanked:
    5259 times
    GMAT Score:
    790
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post Thu Apr 26, 2012 1:32 am
    debonairdrz wrote:
    If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
    what is the length of one side of the triangle in meters?

    (A)6
    (B)8
    (C)4 sqrt(2)
    (D)2 sqrt(3)
    (E)4 sqrt(3)


    I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


    I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

    x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

    3x=(1/2)xh

    Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

    Therefore I now have:

    3x=(1/2)x sqrt(3)(x/2)


    That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

    Any and all help is greatly appreciated.
    Another approach is to plug in the answers, which represent the length of each side of the triangle.
    It is helpful to know the formula for the area of an equilateral triangle:
    A = (s²√3)/4.

    Since p=3s, we get:

    3s = (s²√3)/4.

    For the lefthand side to be equal to the righthand side, the value of s almost certainly will include a factor 4 and a factor of √3.

    Answer choice E: 4√3
    Plugging this value into 3s = (s²√3)/4, we get:
    3(4√3) = ((4√3)²*√3)/4
    12√3 = ((16*3)√3)/4
    12√3 = 12√3.
    Success!

    The correct answer is E.

    _________________
    Mitch Hunt
    GMAT Private Tutor and Instructor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Contact me about long distance tutoring!

    Thanked by: debonairdrz
    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

    Best Conversation Starters
    1 varun289 40 topics
    2 guerrero 21 topics
    3 sana.noor 20 topics
    4 killerdrummer 19 topics
    5 sanaa.rizwan 14 topics
    See More Top Beat The GMAT Members...

    Most Active Experts
    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    		 203 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    		 140 posts
    3 image description Jim@StratusPrep

    Stratus Prep

    		 100 posts
    4 image description Anju@Gurome

    Gurome

    		 99 posts
    5 image description Jon@Admissionado

    Admissionado

    		 49 posts
    See More Top Beat The GMAT Experts