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# The longest straight line that can be inscribed in an isosce

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Director
Joined: 29 Nov 2012
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The longest straight line that can be inscribed in an isosce  [#permalink]

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20 Jul 2013, 05:41
3
8
00:00

Difficulty:

95% (hard)

Question Stats:

42% (01:47) correct 58% (01:57) wrong based on 148 sessions

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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.
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Re: The longest straight line that can be inscribed in an isosce  [#permalink]

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20 Jul 2013, 05:51
1

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]

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19 Aug 2013, 02:40
Hi

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

Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: The longest straight line that can be inscribed in an isosce  [#permalink]

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19 Aug 2013, 03:18
1
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 ??

Consider the figure below:
Attachment:

Area.png [ 2.51 KiB | Viewed 2445 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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Joined: 10 Jul 2013
Posts: 282
Re: The longest straight line that can be inscribed in an isosce  [#permalink]

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19 Aug 2013, 04:57
1
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]

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28 Mar 2016, 19:22
tricky one..thanks bunuel for the picture..
I picked C..as I thought that max we can have is a 45-45-90 triangle..where the base=height...now i see..
Manager
Joined: 01 Mar 2014
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Re: The longest straight line that can be inscribed in an isosce  [#permalink]

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01 Apr 2016, 02:12
Asifpirlo wrote:
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 .

Did pretty much the same thing and got B.P = 20. But got confused as to what implication does the information "no obtuse angles" have. Can you please explain? Thank you.
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Re: The longest straight line that can be inscribed in an isosce  [#permalink]

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16 Feb 2019, 03:04
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Re: The longest straight line that can be inscribed in an isosce   [#permalink] 16 Feb 2019, 03:04
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