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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, 23:40
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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

Spoiler: ::
Attachment:
2019-01-18_1038.png
2019-01-18_1038.png [ 5.28 KiB | Viewed 564 times ]
Spoiler: OA

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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, 06:23
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

Spoiler: ::
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

Originally posted by Archit3110 on 18 Jan 2019, 05:19.
Last edited by Archit3110 on 18 Jan 2019, 06:23, 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, 05:55
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

Spoiler: ::
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, 05:58
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

Spoiler: ::
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, 06:13
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

Spoiler: ::
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.
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PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

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Re: Figure area of the rectangle above is 36. What is the length of diago   [#permalink] 18 Jan 2019, 06:13
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