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

Question

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.

OA:

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\(24\sqrt{2}\)

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srini123 · Answer

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)

lagomez · Answer

same for me  24sqrt2

gintojin · Answer

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.

GMATinsight · Answer

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}

amarinetti · Answer

That 6 correspond to the length MN or to the height of the triangle LMN?

ProfX · Answer

Height I think, since the OA is 24 sqrt 2

Sent from my iPhone using  GMAT Club Forum mobile app

WilDThiNg · Answer

Pardon me but a very fundamental question - Why would the areas of triangles LMN and LNP be different?

Manonamission · Answer

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

KrishnakumarKA1 · Answer

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

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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

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