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How many triangles #5

(10 votes, average: 3.80 out of 5)

January 17, 2013 by puzzler Leave a Comment

1.) How many triangles are there in this triangle ?

how many triangles in this triangle

how many triangles in this triangle

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Answer: There are a total of 47 triangles

How?
Lets count…
By looking at it, first impression is … its very simple, But mind you! its not that easy !!!
So lets stick to the divide and conquer approach, we will divide this triangle into 3 equal triangles(triangle formed by connecting outer side to the center of the circle) and will count the number of triangles in each part and then by taking two or more parts together.

Number of triangles in one part: 4(non overlapping) + 3(overlapping) = 7 * 3 = 21
Number of triangles by taking two parts together: 8 = 8 * 3 = 24
Number of triangles by taking all three parts together: 2

Thus, total number of triangles in this puzzle are : 21+24+2= 47

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