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In the diagram below, if the area of triangle LNP is 32, then what is

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In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 17 Nov 2009, 12:13
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In the diagram below, if the area of triangle LNP is 32, then what is the area of triangle LMN? Note: Figure not drawn to scale.
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OA:
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\(24\sqrt{2}\)


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Last edited by Bunuel on 17 Jun 2015, 02:39, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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kiranicole214 wrote:
Attached is a problem I was given in a GMAT test booklet. Although I have the answer, I still can't figure it out.

It says, in the diagram below, if the area of the tirangle LNP is 32, then what is the area of triangle LMN? The figure in my book is not drawn to scale.


I got \(24sqrt(2)\)

given area of LNP = \((1/2) NP * LP\) = 32 ==> LP = 8

using pythagorean theorem \(LN^2=LP^2+NP^2\)
==> LN = \(sqrt(64+64) = 8sqrt(2)\)

area of LMN =\((1/2) LN * MO\)= \((1/2) * 8 sqrt(2) * 6 = 24 sqrt (2)\)
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 17 Nov 2009, 13:03
srini123 wrote:
kiranicole214 wrote:
Attached is a problem I was given in a GMAT test booklet. Although I have the answer, I still can't figure it out.

It says, in the diagram below, if the area of the tirangle LNP is 32, then what is the area of triangle LMN? The figure in my book is not drawn to scale.


I got \(24sqrt(2)\)

given area of LNP = \((1/2) NP * LP\) = 32 ==> LP = 8

using pythagorean theorem \(LN^2=LP^2+NP^2\)
==> LN = \(sqrt(64+64) = 8sqrt(2)\)

area of LMN =\((1/2) LN * MO\)= \((1/2) * 8 sqrt(2) * 6 = 24 sqrt (2)\)


same for me \(24sqrt2\)
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 16 Jun 2015, 15:52
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In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 17 Jun 2015, 06:30
I am having difficulty understanding the logic path to solving this problem. I see the equations individually and can see the solutions, yet the path for solving this is a challenge for me. Can someone take the time to explain it?
Can you assume LP = 8 since NP=8?
How was the Pythagorean Theorem manipulated to extract an answer?
Where does MO come from.

Respectfully, Puzzled.
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 17 Jun 2015, 07:02
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gintojin wrote:
I am having difficulty understanding the logic path to solving this problem. I see the equations individually and can see the solutions, yet the path for solving this is a challenge for me. Can someone take the time to explain it?
Respectfully, Puzzled.


About the Area of Triangle, There is only one Basic

i.e. Area of Triangle = (1/2) Base of Triangle x Height of triangle

You must Understand that Base can be any side of the triangle but Height in each case will be the perpendicular Distance of Third Vertex pf Triangle from the Base taken

i.e. Take area of Triangle LNP and Consider tha Base= LP, Then Height will be the Perpendicular Distance of LP from N i.e. NP=8

i.e. Area of Triangle LNM = (1/2) x LP x 8 = 32 (Given)

i.e. LP = 8

Now LNP is a right angle Triangle therefore we can apply Pythagorus Theorem to calculate Hypotenuse of the Triangle

i.e. LN^2 = 8^2 + 8^2
i.e. LN = \(8\sqrt{2}\)

Now Area of LNM = (1/2) LN x 6 = \((1/2) * 8\sqrt{2} * 6 = 24\sqrt{2}\)
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 30 Sep 2016, 11:16
That 6 correspond to the length MN or to the height of the triangle LMN?
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 30 Sep 2016, 11:22
Height I think, since the OA is 24 sqrt 2


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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 19 Oct 2016, 16:03
Pardon me but a very fundamental question - Why would the areas of triangles LMN and LNP be different?
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 22 Oct 2016, 06:01
Area of triangle LMP = 32 = 1/2.b.h => b = 8

LN = Sq rt (8^2 + 8^2) = 8 sq rt 2

Area of triangle LNM = 1/2. 8 sq rt 2 . 6 = 24√2
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Re: In the diagram below, if the area of triangle LNP is 32, then what is [#permalink]

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New post 01 Mar 2017, 01:14
Area of triangle LNP = ½ * LP*NP
or 32 = ½ *LP*4
or LP = 8.
Therefore using Pythagoras in triangle LNP we can say that the value of LN = 8 √2
Area of LMN = ½ *6*8 √2 = 24 √2
Re: In the diagram below, if the area of triangle LNP is 32, then what is   [#permalink] 01 Mar 2017, 01:14
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In the diagram below, if the area of triangle LNP is 32, then what is

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