A triangle is made up of 2 red sticks and 1 blue stick. The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given.

Question

A triangle is made up of 2 red sticks and 1 blue stick. The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given.

Vedantu Content Team · Accepted Answer

Hint: In this question, we are given a figure of triangles and length of the sticks used to make the triangles. We have been told that each triangle is made up of 2 red sticks and 1 blue stick. We are required to make an expression of the total length using this information. First, count the number of red and blue sticks. Multiply them with their measurements. Then, add both of them together. The result will be the required expression.Complete step-by-step solution:We have been told that the triangles in the given figures are made up of one blue and two red sticks. The length of red stick is $r$ and that of blue stick is $b$. So, I have put the labels in the given diagram as below:

If we count the number of triangles, we can see that there are $12$ triangles. We will also calculate the number of red and blue sticks in the given figure.Number of red sticks = $18$Number of blue sticks = $6$Also, we know that the length of each red stick is r and each blue stick is b.Length of red stick = $18r$Length of blue stick = $6b$Therefore, total length of sticks = $18r + 6b$Hence, the required expression for the total length of sticks is $6\left( {3r + b} \right)$.Note: The students often count the number of triangles and then using this number, they count the number of red and blue sticks. This is a wrong method and will give you the wrong number of red and blue sticks. This is because some of the sticks overlap with each other and will give you a correct impression if you count them individually. For example: In this picture, there are 12 triangles. If using this we would have to calculate, we will see that each triangle has 2 red sticks. So, total red sticks $ = 12 \times 2 = 24$And each triangle has 1 blue stick. So, total blue sticks =$12 \times 1 = 12$These are wrong measurements.