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Geometry

This topic has 3 expert replies and 2 member replies
vinay1983 Legendary Member
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Geometry

Post Wed Sep 04, 2013 5:17 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the approximate perimeter of a square that has a diagonal of length 6?


    1. 4
    2. 13
    3. 17
    4. 20
    5. 24

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    Post Wed Sep 04, 2013 5:39 am
    vinay1983 wrote:
    What is the approximate perimeter of a square that has a diagonal of length 6?


    A. 4
    B. 13
    C. 17
    D. 20
    E. 24
    Let x be the length of one side of the square.
    So, 2 sides of the square and the diagonal form a right triangle, which means we can apply the Pythagorean formula to get:
    x² + x² = 6²
    2x² = 36
    x² = 18
    x = √18 = 3√2

    There are 4 sides, to the perimeter = 3√2 + 3√2 + 3√2 + 3√2 = 12√2

    IMPORTANT: There are 3 useful square root approximations you should memorize for the GMAT.
    √2 is approximately 1.4
    √3 is approximately 1.7
    √5 is approximately 2.2

    So, 12√2 = approximately 12(1.4)
    Since 12(1.5) = 18, we know that 12(1.4) is a little less than 18. So, choose C

    Cheers,
    Brent

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    Post Wed Sep 04, 2013 7:52 am
    vinay1983 wrote:
    What is the approximate perimeter of a square that has a diagonal of length 6?


    1. 4
    2. 13
    3. 17
    4. 20
    5. 24
    The diagonal of a square = s√2 ≈ (7/5)s.
    We can plug in the answers for the perimeter of the square.

    Answer choice C: 17
    Here, s = 17/4, implying that the diagonal ≈ (7/5)(17/4) ≈ 119/20 ≈ 6.

    The correct answer is C.

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    vinay1983 Legendary Member
    Joined
    14 Aug 2013
    Posted:
    643 messages
    Followed by:
    6 members
    Thanked:
    48 times
    Target GMAT Score:
    650+
    Post Wed Sep 04, 2013 7:59 am
    GMATGuruNY wrote:
    vinay1983 wrote:
    What is the approximate perimeter of a square that has a diagonal of length 6?


    1. 4
    2. 13
    3. 17
    4. 20
    5. 24
    The diagonal of a square = s√2 ≈ (7/5)s.
    We can plug in the answers for the perimeter of the square.

    Answer choice C: 17
    Here, s = 17/4, implying that the diagonal ≈ (7/5)(17/4) ≈ 119/20 ≈ 6.

    The correct answer is C.
    Mitch,

    I was thinking of this approach to the soulution, but I want to know how you got (7/5)s?

    _________________
    You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

    Post Wed Sep 04, 2013 12:36 pm
    vinay1983 wrote:
    GMATGuruNY wrote:
    vinay1983 wrote:
    What is the approximate perimeter of a square that has a diagonal of length 6?


    1. 4
    2. 13
    3. 17
    4. 20
    5. 24
    The diagonal of a square = s√2 ≈ (7/5)s.
    We can plug in the answers for the perimeter of the square.

    Answer choice C: 17
    Here, s = 17/4, implying that the diagonal ≈ (7/5)(17/4) ≈ 119/20 ≈ 6.

    The correct answer is C.
    Mitch,

    I was thinking of this approach to the soulution, but I want to know how you got (7/5)s?
    √2 ≈ 1.4 = 14/10 = 7/5.
    Thus, the diagonal of a square = s√2 ≈ (7/5)s.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

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    Post Wed Sep 04, 2013 11:28 pm
    Hi Vinay,

    All of the "math approaches" are correct, but you might find that TESTING THE ANSWERS could get you the correct answer in a shorter period of time.

    Since the question asks about the perimeter of a square, we need 4(something).

    We're told that the diagonal = 6, so answers A and B are too small and Answer E is too big.

    Between C and D....

    Answer D would mean that each side = 5, which means that the diagonal would have to be 5(root2). 5(root2) does NOT = 6, so the answer MUST be C.

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

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