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Figure area of the rectangle above is 36. What is the length of diago

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Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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New post 17 Jan 2019, 22:40
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Figure area of the rectangle above is \(36\sqrt{3}\). What is the length of diagonal AC?

A 6
B 12
C 18
D 24
E 30

Attachment:
2019-01-18_1038.png
2019-01-18_1038.png [ 5.28 KiB | Viewed 397 times ]

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Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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New post Updated on: 18 Jan 2019, 05:23
Bunuel wrote:
Image
Figure area of the rectangle above is 36. What is the length of diagonal AC?

A 6
B 12
C 18
D 24
E 30

Attachment:
2019-01-18_1038.png


x* xsqrt3 = 36 sqrt 3
x= 6
30:60:90
x:xsqrt3: 2x
diagonal ; 2* 6 = 12
IMO B
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Originally posted by Archit3110 on 18 Jan 2019, 04:19.
Last edited by Archit3110 on 18 Jan 2019, 05:23, edited 1 time in total.
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Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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New post 18 Jan 2019, 04:55
1
Bunuel wrote:
Image
Figure area of the rectangle above is 36. What is the length of diagonal AC?

A 6
B 12
C 18
D 24
E 30

Attachment:
2019-01-18_1038.png


The diagonal divides the rectangle in two equal parts and each is a 30-60-90 triangle, where sides are 1:\(\sqrt{3}\):2.
If we take the common ratio as x, the sides are x, \(\sqrt{3}\)x, and 2x.

Now area of rectangle is \(x*\sqrt{3}\)x=36......\(3x^4=36^2....x^4=4^4*9^4/3=\)
x will come out to be some crazy number, which will surely not be an integer..
so I believe he area should be \(36\sqrt{3}\), which will give x as 6 and diagonal will be 2x = 2*6=12..
Bunuel, pl relook in the question
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Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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New post 18 Jan 2019, 04:58
chetan2u wrote:
Bunuel wrote:
Image
Figure area of the rectangle above is 36. What is the length of diagonal AC?

A 6
B 12
C 18
D 24
E 30

Attachment:
2019-01-18_1038.png


The diagonal divides the rectangle in two equal parts and each is a 30-60-90 triangle, where sides are 1:\(\sqrt{3}\):2.
If we take the common ratio as x, the sides are x, \(\sqrt{3}\)x, and 2x.

Now area of rectangle is \(x*\sqrt{3}\)x=36......\(3x^4=36^2....x^4=4^4*9^4/3=\)
x will come out to be some crazy number, which will surely not be an integer..
so I believe he area should be \(36\sqrt{3}\), which will give x as 6 and diagonal will be 2x = 2*6=12..
Bunuel, pl relook in the question

chetan2u
Even I was taken aback seeing the value of x.. seems there is definitely some value error in either answer options or the area of rectangle given..

Bunuel please look into it & advise..
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Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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New post 18 Jan 2019, 05:13
chetan2u wrote:
Bunuel wrote:
Image
Figure area of the rectangle above is 36. What is the length of diagonal AC?

A 6
B 12
C 18
D 24
E 30

Attachment:
2019-01-18_1038.png


The diagonal divides the rectangle in two equal parts and each is a 30-60-90 triangle, where sides are 1:\(\sqrt{3}\):2.
If we take the common ratio as x, the sides are x, \(\sqrt{3}\)x, and 2x.

Now area of rectangle is \(x*\sqrt{3}\)x=36......\(3x^4=36^2....x^4=4^4*9^4/3=\)
x will come out to be some crazy number, which will surely not be an integer..
so I believe he area should be \(36\sqrt{3}\), which will give x as 6 and diagonal will be 2x = 2*6=12..
Bunuel, pl relook in the question


Fixed the typo. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Figure area of the rectangle above is 36. What is the length of diago   [#permalink] 18 Jan 2019, 05:13
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