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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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A
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C
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  25% (medium)

Question Stats:

67% (01:49) correct 33% (02:39) wrong based on 49 sessions

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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

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

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

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

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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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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