MathematicsHow many triangles are there in the following figure?

How many triangles are there in the following figure?


  1. A
    19 
  2. B
    21 
  3. C
    27 
  4. D
    48 

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    Solution:

    Concept: Consider 4 levels of the triangles. Count the small triangles from every 4 levels. Now manage each level like(1+2) ,(2+3) ,(3+4) ,(1+2+3) ,(2+3+4) and (1+2+3+4)  levels and get the no. of triangles. To get the total number of triangles, we have to add all three together.
    At the first level =1 triangle
    Second level =3 triangles
    The third level =5 triangles
    The fourth level = 7 triangles
    Merging level (1, 2) , then (1, 2, 3) and then (1, 2, 3, 4): 3 triangles Merging levels (2, 3): 2 triangles
    Merging levels 3 and 4: 4 triangles
    Merging levels 2, 3, and 4 together: 2 triangles.
    So, a total number of triangles =1+3+5+7+3+2+4+2=27.
    Thus, there are a total of 27 triangles.
    Hence, the correct answer is option (3) .
     
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