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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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Difficulty:   25% (medium)

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

HideShow timer Statistics 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 [ 5.28 KiB | Viewed 564 times ]

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

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Bunuel wrote: 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.
Math Expert V
Joined: 02 Aug 2009
Posts: 8023
Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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1
Bunuel wrote: 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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Joined: 18 Aug 2017
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Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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chetan2u wrote:
Bunuel wrote: 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..
Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: Figure area of the rectangle above is 36. What is the length of diago  [#permalink]

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chetan2u wrote:
Bunuel wrote: 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.
_________________ 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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