help

This topic has 6 expert replies and 3 member replies
sana.noor Legendary Member Default Avatar
Joined
18 Jun 2012
Posted:
510 messages
Followed by:
19 members
Thanked:
42 times
Test Date:
October '13
Target GMAT Score:
740

help

Post Fri Aug 23, 2013 11:12 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In the figure Shown,two identical squares are inscibed in the rectangle.if the area of the rectangle is 36 Sq. Units,then what is the perimeter of each Square??



    i dont have its answer

    _________________
    Work hard in Silence, Let Success make the noise.

    If you found my Post really helpful, then don't forget to click the Thank/follow me button. Smile

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sat Aug 24, 2013 12:21 am
    Hi sana.noor,

    In the drawing that you provided, you should notice that:

    the width of the rectangle = 2(square's diagonal)
    the height of the rectangle = 1(square's diagonal)

    Using square "rules", the diagonal = x(root2)

    So the area of the rectangle = (width)(height) = 2(x(root2))^2 = 36

    Let's simplify:
    (x(root2))^2 = 18
    x^2(2) = 18
    x^2 = 9
    x = 3

    So the perimeter of each square = 3(4) = 12

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: sana.noor
    Post Sat Aug 24, 2013 5:36 am
    sana.noor wrote:


    In the figure shown, two identical squares are inscribed in the rectangle. If the area of the rectangle is 36, what is the perimeter of each square?

    Here's a slightly different approach:
    Since the height of the rectangle and the diagonal of a square are the same length, let's let x = height of rectangle


    Since the width of the rectangle is equal to the length of two square diagonals, then the width of the rectangle = 2x.


    The area of the rectangle is 36.
    So, (base)(height) = 36
    (2x)(x) = 36
    2x²= 36
    x²= 18
    x = √18

    NOTE: There's no need to simplify √18 at this point (you'll see why shortly)

    If the height of the rectangle is √18, then the length of the red line (shown below) must equal √18/(2)


    Likewise, the other red line has length √18/(2)


    If we let y = the length of the hypotenuse, then the Pythagorean Theorem states that...


    Now solve this equation for y.


    If y = 3, then the perimeter of one square = (4)(3) = 12

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    happy888 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    10 Jan 2016
    Posted:
    4 messages
    Post Sun Jan 10, 2016 3:07 pm
    Hi Brent,

    I didn't understand why 1/4th length of the rectangle is squareroot18/2

    Thanks

    Post Sun Jan 10, 2016 8:33 pm
    Hi happy888,

    The 'key' to this whole question is in realizing that the width and height of the rectangle can be expressed in terms of the DIAGONAL of each of the SQUARES. Are you able to follow the 'set-up' of the calculations involved?

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Post Sun Jan 10, 2016 9:38 pm
    happy888 wrote:
    Hi Brent,

    I didn't understand why 1/4th length of the rectangle is squareroot18/2

    Thanks
    Once we know that the height of the rectangle is √18, then HALF of that is (√18)/2


    I hope that helps.

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    happy888 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    10 Jan 2016
    Posted:
    4 messages
    Post Wed Jan 13, 2016 4:40 am
    Hi,

    Got it

    Thanks Smile

    hotcool030 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    07 May 2017
    Posted:
    5 messages
    Post Sun Jul 02, 2017 4:34 am
    I solved it in a very easy way.
    Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
    And one diagonal of square = width of rectangle.
    So, as Length x Width = 36,
    we can say (2 * root2x)* (root2x) = 36
    x = 3
    Perimeter of square = 12
    Smile

    GMAT/MBA Expert

    Post Tue Jul 04, 2017 11:57 pm
    hotcool030 wrote:
    I solved it in a very easy way.
    Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
    And one diagonal of square = width of rectangle.
    So, as Length x Width = 36,
    we can say (2 * root2x)* (root2x) = 36
    x = 3
    Perimeter of square = 12
    Smile
    Nice approach! For anyone needing a visual, this is the same approach the great Brent uses above.

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    Post Fri Jul 07, 2017 3:27 pm
    The squares just take up half the rectangle. There are a few ways to see that. For example, if you divide up the picture into a grid of 8 squares, as I did below, you can see that half of each grid zone is taken up by part of a square, and the other half is taken up by non-square.

    So the area of the squares is half the total area of the rectangle, so the area of the two squares is 36/2 = 18, and the area of each square is 9. So the squares measure 3 by 3, and the perimeter of each is 12.
    Attachments

    This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.


    _________________
    If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

    Best Conversation Starters

    1 AbeNeedsAnswers 30 topics
    2 amontobin 16 topics
    3 richachampion 12 topics
    4 NandishSS 8 topics
    5 rsarashi 5 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Matt@VeritasPrep

    Veritas Prep

    74 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    72 posts
    3 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    66 posts
    4 image description DavidG@VeritasPrep

    Veritas Prep

    65 posts
    5 image description Jay@ManhattanReview

    Manhattan Review

    55 posts
    See More Top Beat The GMAT Experts