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by vinay1983 » 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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by Brent@GMATPrepNow » 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 [spoiler]C
[/spoiler]
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by GMATGuruNY » 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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by vinay1983 » 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?
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by GMATGuruNY » 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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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
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by [email protected] » 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.

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