Different frames are formed using a triangular structure as shown. Find the rule that will give the number of sticks in terms of the number of triangle frames. Also, find the number of sticks used in 9 triangle frames.

Open in App

Solution

Solution:

The first figure consists of 1 triangle made up of 3 sticks.

The second figure consists of 3 triangles made up of 7 sticks.

The third figure consists of 5 triangles made up of 11 sticks.
So, going by the pattern, the generalized rule is that the number of sticks is one more than twice the number of triangles.

Hence, the pattern is 2n + 1, where n is the number of triangles.
We have to find the number of sticks in 9 triangle frames that means n = 9.
So, number of sticks = 2 × 9 + 1
= 18 + 1
= 19 sticks.

Suggest Corrections

Similar questions

Q. Different frames are formed using a C-shaped structure as shown. Each C-shaped structure is made of wooden strips. Find the rule that will give the number of wooden strips in terms of the number of C-shaped frames.

Alex makes a C-shaped frame using wooden strips. He subsequently makes 2 C-shaped, 3 C-shaped frames, and so on, as shown in the figure. Find the rule that will give the number of wooden strips in terms of the number of C-shaped frames.

The given figure gives a match stick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

(a) (b) (c) (d)

Q. Find the rule which gives the number of sticks used for creating the following pattern. Also find the number of stick used to from a group of 50 shapes.

(2 marks)

Q. Find the rule which gives the number of sticks used to form a pattern of the letter W.

Join BYJU'S Learning Program

Different frames are formed using a triangular structure as shown. Find the rule that will give the number of sticks in terms of the number of triangle frames.​​ Also, find the number of sticks used in 9 triangle frames.​

Different frames are formed using a triangular structure as shown. Find the rule that will give the number of sticks in terms of the number of triangle frames. Also, find the number of sticks used in 9 triangle frames.