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
Geometry
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Let x be the length of one side of the square.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
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]
Cheers,
Brent
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The diagonal of a square = s√2 ≈ (7/5)s.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
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
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Mitch,GMATGuruNY wrote:The diagonal of a square = s√2 ≈ (7/5)s.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
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.
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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√2 ≈ 1.4 = 14/10 = 7/5.vinay1983 wrote:Mitch,GMATGuruNY wrote:The diagonal of a square = s√2 ≈ (7/5)s.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
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.
I was thinking of this approach to the soulution, but I want to know how you got (7/5)s?
Thus, the diagonal of a square = s√2 ≈ (7/5)s.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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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
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