+0  
 
+1
80
1
avatar+117 

This one is another question thati need help with,

petri  Oct 4, 2018
 #1
avatar+92376 
+2

Both triangles  PNQ and LPQ  have the same altitude  ( PQ)

 

So....triangles under the same altitude are to each other as their bases...and since  the area of LPQ is twice that of PNQ...its base (PL)  must be twice as  long as the base of PNQ  =  (NP)

Therefore....PL  = 2NP

 

And since PQ is parallel to LM ⇒    NL : NP  =  LM /PQ =   [ NP + PL ] / NP  = [NP + 2NP] / NP  = 3NP / NP  = 3

Therfore...LM : PQ  = 3 : 1

 

So...the scale factor  of triangle NLM  to triangle NPQ  is 3 : 1  = 3

 

And the area of triangle   NLM  = Area of triangle NPQ * scale factor^2  = 8 * 3^2  = 8 * 9  = 72 units^2

 

So....  Area of LQM  =    [ area of NLM  - combined areas of (PNQ + LPQ)  ] 

 

72  - [ 8 + 16 ]  = 

 

72 - 24  =

 

48 units^2

 

 

cool cool cool

CPhill  Oct 4, 2018

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