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Geometry

This topic has 4 expert replies and 1 member reply
vinay1983 Legendary Member
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Geometry

Post Wed Sep 04, 2013 5:17 am
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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GMAT/MBA Expert

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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GMAT/MBA Expert

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.

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GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
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GMAT/MBA Expert

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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GMAT/MBA Expert

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.

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

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vinay1983 Legendary Member
Joined
14 Aug 2013
Posted:
643 messages
Followed by:
6 members
Upvotes:
48
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!

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