Question

The sticks of same length are used to form a triangle as shown below.if 87 such sticks are used then how many triangles can be formed? 

Answer 1

Refer to the image attached.

First triangle is formed with 3 sticks.

But any subsequent triangle can be formed with 2 sticks.

Since, first triangle uses 3 sticks.

therefore, remaining sticks = 87-3 = 84

With 84 sticks, 42 triangles can be formed.

So, total number of triangles formed = 42 + 1 = 43.

Therefore, 43 triangles are formed with 87 sticks.

Answer 2

After making a triangle with 3 stick then in continuous it needs only 2 stick to form the triangle

Then 87-3=84 triangle is there so 842 =  42 sticks are used but 1 is already formed by 3 stick so it is 42+1=43

Or Simply use this formula:-

2n+1=87

2n=87-1

2n=86

n=43.

Hence 43 no of triangle can be made by the 87 sticks.