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If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim

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If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post Updated on: 30 May 2017, 00:08
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:50) correct 30% (03:21) wrong based on 104 sessions

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If a right angled isosceles triangle has an area of 2x^2 + 2x + 1/2. What is its perimeter?

A. 3(x + 1)
B. 2^1/2(x^2 + 1)
C. (2^1/2 x - 1)(2x + 1)
D. (2 + 2^1/2)(2x + 1)
E. 2x + 2^1/2

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Originally posted by AnkitK on 21 Jun 2011, 03:07.
Last edited by abhimahna on 30 May 2017, 00:08, edited 1 time in total.
Edited the question
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post Updated on: 21 Jun 2011, 04:51
3
AnkitK wrote:
If an isosceles triangle an area of 2x^2+2x+1/2.What is its perimeter?
A.3(x+1)
B.2^1/2(x^2+1)
C.(2^1/2 x-1)(2x+1)
D.(2+2^1/2)(2x+1)
E.2x+2^1/2


I think there is some mistake in typing the question, you can not answer this question unless it is RIGHT ANGLED ISOSCELES TRIANGLE

Now, if we take the correction into consideration then following will be the diagram
Attachment:
D.jpg
D.jpg [ 24.33 KiB | Viewed 2443 times ]


Now, In the given triangle AB = BC ...isosceles triangle
Hence angle A = angle C = 45
And angle B = 90

Now area of triangle = 1/2 *AB* BC
thus \(2x^2+2x+1/2 = 1/2 * AB^2\)
Hence \(AB^2 = 4x^2+4x+1\)
\(AB^2 = (2x+1)^2\)

Hence AB=BC = 2x+1

Now AC is an hypotenuse of the triangle
hence AC = 2^1/2 AB = 2^1/2 (2x+1)

Now perimeter = 2AB + AC = 2 (2x+1) + 2^1/2 (2x+1)
= (2x+1) (2+2^1/2)

Hence Option D is an answer

Originally posted by vyassaptarashi on 21 Jun 2011, 04:39.
Last edited by vyassaptarashi on 21 Jun 2011, 04:51, edited 2 times in total.
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post 21 Jun 2011, 04:47
Superb vyassa!I solved it but took arnd 10 min.I hate it .Yeh that was an typo..sry.
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post 21 Jun 2011, 04:58
Thanks, I tried this one but failed.. Good explanation!
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post 08 Mar 2016, 07:51
AnkitK wrote:
If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perimeter?

A. 3(x + 1)
B. 2^1/2(x^2 + 1)
C. (2^1/2 x - 1)(2x + 1)
D. (2 + 2^1/2)(2x + 1)
E. 2x + 2^1/2


Awesome Question
I guess the question needs to be edited and we need to make it a right angled Isosceles triangle and then the sides we get will be 2x+1,2x+1 as the equal sides and the hypotenuse will be
√2 * 2x+1
hence D
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim  [#permalink]

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New post 29 May 2017, 00:34
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Re: If an isosceles triangle an area of 2x^2 + 2x + 1/2. What is its perim   [#permalink] 29 May 2017, 00:34
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