Find the number of triangles in the above diagram?

(A) 32 (B)23 (C)26
(D) 27 (E) 16

Solution follows here:

__Sollution__
First
we start from each of the 3-corners.

From
corner-1 : (1,2,3), (1,4,6), (1,7,10), (1,11,15) --- 4

From
corner-11 : (11,4,13), (11,2,14) ---
2

From
corner-15 : (15,6,13), (15,3,12) ---
2

Now
we count all the smallest triangles
excluding (1,2,3) which is already considered above:

(2,4,5), (2,3,5), (3,5,6) ---3

(4,7,8), (4,5,8), (5,8,9), (5,6,9), (6,9,10) ---5

(8,12,13),(8,9,13),(9,13,14) ---3

Now
by considering “middle 3-points” of each side of the outer triangle, we get the
following:

(2,7,9),
(3,8,10), (12,5,14) ---3

Now
by considering “single middle point” of each side of the outer triangle, we get
the following:

(4,6,13) ---1

So
the total number of triangles = 4+2+2+3+5+3+3+1 = 23

**Answer (B)**

26 is the answer

ReplyDeletecsat question answer is 23..here picture is wrong

ReplyDeleteyes Anonymous, you are right, corrected one will be uploaded now..., thanks for that

ReplyDelete