UPSC CSE Prelims 2011
Consider the following figure and answer the item that follows:
What is total number of triangles in the above grid?
EXPLANATION
Correct Option (C)
The total number of triangles in the given grid is determined by systematically enumerating triangles of varying sizes. This involves categorizing and summing all possible triangles based on the number of fundamental unit triangles they comprise.
- Smallest Triangles: These are the individual, irreducible triangles within the figure. There are 12 such triangles.
- Triangles of the second size: These are larger triangles, each formed by combining four of the smallest triangles. There are 7 such triangles.
- Triangles of the third size: These are even larger triangles, each formed by combining nine of the smallest triangles. There are 3 such triangles.
- Largest Triangle: This refers to the single, outermost triangle that encompasses the entire grid. There is 1 such triangle.
The cumulative sum of these counts yields the total number of triangles:
Total Triangles = 12 + 7 + 3 + 1 = 23.
Incorrect Options:
Options A (27), B (26), and D (22) are incorrect because they do not reflect the accurate systematic enumeration of all triangles within the grid. A precise count, categorizing triangles by their constituent unit sizes, yields a total of 23 triangles, as detailed in the explanation for the correct option.
