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The longest straight line that can be inscribed in an isosce

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The longest straight line that can be inscribed in an isosce [#permalink] New post 20 Jul 2013, 04:41
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Question Stats:

46% (02:09) correct 54% (01:41) wrong based on 117 sessions
The longest straight line that can be inscribed in an isosceles triangle with area 10 and no obtuse angles is

A. less than 5

B. greater than or equal to 5, but less than 7.5

C. greater than or equal to 7.5, but less than 10

D. greater than or equal to 10, but less than 20.

E. greater than 20.
[Reveal] Spoiler: OA

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Re: The longest straight line that can be inscribed in an isosce [#permalink] New post 20 Jul 2013, 04:51
Answer Option E.

No obtuse angle. Lets say its a right angled triangle with height 20 & base 1 (so area is 20X1X0.5). Definitely we can inscribe a line greater than 20. Or we can take the height as 40 & base as 0.5 too.
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Re: The longest straight line that can be inscribed in an isosce [#permalink] New post 19 Aug 2013, 01:40
Hi

How can the answer be E.
Doesn't the question says that its an isosceles triangle ??

Please help !!
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Re: The longest straight line that can be inscribed in an isosce [#permalink] New post 19 Aug 2013, 02:18
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ankitD wrote:
The longest straight line that can be inscribed in an isosceles triangle with area 10 and no obtuse angles is

A. less than 5
B. greater than or equal to 5, but less than 7.5
C. greater than or equal to 7.5, but less than 10
D. greater than or equal to 10, but less than 20.
E. greater than 20.

Hi

How can the answer be E.
Doesn't the question says that its an isosceles triangle ??

Please help !!


Consider the figure below:
Attachment:
Area.png
Area.png [ 2.51 KiB | Viewed 1132 times ]
Area=1/2*1/2*40=10 --> the longest straight line that can be inscribed > 40 > 20.

Hope it helps.
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Re: The longest straight line that can be inscribed in an isosce [#permalink] New post 19 Aug 2013, 03:57
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fozzzy wrote:
The longest straight line that can be inscribed in an isosceles triangle with area 10 and no obtuse angles is

A. less than 5

B. greater than or equal to 5, but less than 7.5

C. greater than or equal to 7.5, but less than 10

D. greater than or equal to 10, but less than 20.

E. greater than 20.


Let perpendicular = P
base = B

Now, 1/2 . B . P = 10
or, B . P = 20
Possibilities of the lengths B = 20 then P = 1
or, B = 200 And P = 1/10 Thus we can extract various values over 20 . So longest is more than 20 .
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Re: The longest straight line that can be inscribed in an isosce [#permalink] New post 23 Mar 2015, 11:27
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Re: The longest straight line that can be inscribed in an isosce   [#permalink] 23 Mar 2015, 11:27
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