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In a triangle ABC, AC=2. Is BC>

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In a triangle ABC, AC=2. Is BC>  [#permalink]

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New post 14 Jul 2017, 18:40
3
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

26% (02:03) correct 74% (01:47) wrong based on 50 sessions

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In a \(\triangle\) ABC, \(AC=2\). Is \(BC >3 \sqrt{2}\)?

1) \(\triangle\) ABC is obtuse
2) \(\triangle\) ABC is isosceles
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In a triangle ABC, AC=2. Is BC>  [#permalink]

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New post 14 Jul 2017, 20:28
1
Tan2017 wrote:
In a \(\triangle\) ABC, \(AC=2\). Is \(BC >3 \sqrt{2}\)?

1) \(\triangle\) ABC is obtuse
2) \(\triangle\) ABC is isosceles


obtuse triangle is a triangle that has one angle greater than 90 degree.
isosceles triangle is a triange with two equal sides.

(1) We cant know whether BC is greater than \(3\sqrt{2}\) or not. Insufficient.

Attachment:
statement 1.png
statement 1.png [ 4.96 KiB | Viewed 1040 times ]


(2) As (2), insufficient.

Attachment:
statement 2.png
statement 2.png [ 5.16 KiB | Viewed 1032 times ]


Combine (1) and (2):

Attachment:
combine (1) and (2).png
combine (1) and (2).png [ 3.77 KiB | Viewed 1013 times ]


Case 1: A > 90.
BC < AB + AC = 4 < \(3\sqrt{2}\). Sufficient.

Case 2: B > 90
C < B => BC < AC = 2 < \(3\sqrt{2}\)

The answer is C
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Re: In a triangle ABC, AC=2. Is BC>  [#permalink]

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New post 14 Jul 2017, 20:38
Tan2017 wrote:
In a \(\triangle\) ABC, \(AC=2\). Is \(BC >3 \sqrt{2}\)?

1) \(\triangle\) ABC is obtuse
2) \(\triangle\) ABC is isosceles



Hi...

I statement I tells us that ABC is obtuse.
BC can take any value..
Insufficient..

II this tells us that ABC is isosceles triangle.
If 2 is the SAME side..
Two sides are 2,2 and third side will be less than 4. So ans NO as 3√2>4.
If 2 is the THIRD side, ans can be yes or no.. 7,7,2 OR 3,3,2
Insufficient

Combined

It is obtuse isosceles triangle.
If 2 is the EQUAL sides... The third side will be <2+2... Ans NO
If 2 is the UNEQUAL side.... The other two will be<2, as the side OPPOSITE the largest angle ( here obtuse angle) will be the largest..
Again ans will be NO

Sufficient

C
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Re: In a triangle ABC, AC=2. Is BC>   [#permalink] 14 Jul 2017, 20:38
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