Geometry problem..please help me out

[Sebbl99]

help guys, the books says 24sqrt(2) is the correct answer, but I can t come up with it, tried every form including 1:1:sqrt2 and pythagoras etc, maybe its too late in the night, help me out of my misery

In the diagram given, if the area of triange LNP is 32, then what is the area of triangle LMN?

[just-do-it]

A of triangle LNP = 1/2 * LP * NP = 32 with NP=8 we get LP= 8

so LNP is isosceles right angled triangle.
so LN = 8 sqrt ( 2)

now aread of LMN = 1/2 * LN * 6 = 1/2 * 8 sqrt ( 2) * 6 = 24 sqrt (2).

did u do any calculation mistake ?

[Sebbl99]

thx so much, now it seems so obvious, but it was inextricable yesterday night , guess I was too tired, I even calculated with 8 s(qrt2) but still couldn t come up with the proper answer-thx anyway

[tnclimber]

I am having an issue with this problem as well.

I was able to work it down to

(8 sqroot(2) * 6)/2

from here how do I get 24 sqrroot(2).

I was able to do the math to get 33.93 but i dont know how to keep it it the non decimal form.

Thanks