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kiranicole214
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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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gintojin
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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That 6 correspond to the length MN or to the height of the triangle LMN?
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Height I think, since the OA is 24 sqrt 2


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