ABC is an isosceles triangle having right angle at B, and is made up of several isosceles triangles
Q17 What is the total number of triangles in the figure?
ABC is an isosceles triangle having right angle at B, and is made up of several isosceles triangles
Q17 What is the total number of triangles in the figure?
The correct option is D (d) 48
Surely, you would be able to see many triangles in the figure. Perhaps too many. You would do better by organizing the triangles in same pattern.
In one pattern we would look at the different layers of triangles/squares etc. as follows:
In the bottom layer there are nine triangles
In the higher layers:
First upper deck has seven triangles.
Second upper deck has five triangles.
Third upper deck = three triangles
Top deck = one triangle
Hence in single layer you get 25 triangles. Next, let us combine two layers again starting from the bottom, i.e. bottom + first upper deck
Thus, combining two layers from the bottom upwards you would get 6 + 4 + 2 + 1=13 triangles.
Now taking three layers at a time you would see 3 + 2 + 1 = 6. Finally, taking four layers at a time you would get 2 + 1 = 3. At last you have the largest triangle.
Thus, total number is 25 + 13 + 6 + 3 + 1 = 48 triangles.
(d) 48
Surely, you would be able to see many triangles in the figure. Perhaps too many. You would do better by organizing the triangles in same pattern.
In one pattern we would look at the different layers of triangles/squares etc. as follows:
In the bottom layer there are nine triangles
In the higher layers:
First upper deck has seven triangles.
Second upper deck has five triangles.
Third upper deck = three triangles
Top deck = one triangle
Hence in single layer you get 25 triangles. Next, let us combine two layers again starting from the bottom, i.e. bottom + first upper deck
Thus, combining two layers from the bottom upwards you would get 6 + 4 + 2 + 1=13 triangles.
Now taking three layers at a time you would see 3 + 2 + 1 = 6. Finally, taking four layers at a time you would get 2 + 1 = 3. At last you have the largest triangle.
Thus, total number is 25 + 13 + 6 + 3 + 1 = 48 triangles.
