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ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point is selected at random in the square. Calculate the probability that it will liein the triangle MCN.

 Feb 14, 2020
 #1
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See the diagram :

 

 

Let  the side of the square =  S

Then the area of the square = S^2

 

Note that MC, NC = (1/2)S  

And triangle MCN  is a right triangle  with MN, NC  the legs

The  area of this triangle =  (1/2) (Product of the leg lengths)  =  (1/2) [ (1/2S * (1/2) S [ =  (1/8) S^2

 

So....the  probability  that  the point lies within triangle MCN =

 

Area of triangle MCN

_________________  = 

Area of square

 

(1/8) S^2                  

________      =       

    S^2   

 

 

      1

_______

      8           

 

 

cool cool cool

 Feb 14, 2020

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