Question

Radha is drawing a dot rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has nine dots in a row. How many dots will her rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Answer 1

Hint:
Here we just have to observe the pattern once. Then it changes according to the requirement. How? See in 1 row there are 9 dots. So in 2 rows there will be 18 dots. That is, the number of dots is equal to the number of rows multiplied by the number of dots in a row. So let’s find the dots in remaining rows.

Complete step by step solution:
Given that in a row there are 9 dots.
°°°°°°°°°
Now as we have discussed in 2 rows there will be 18 dots.
°°°°°°°°°
°°°°°°°°°
So it indicates that number of dots in r rows is equal to the product of number of rows and number of dots in a row that is,
  \[ \Rightarrow number{\text{ }}of{\text{ }}dots{\text{ }}in{\text{ }}r{\text{ }}rows = r \times 9\]
Number of dots in 8 rows is,
\[ \Rightarrow number{\text{ }}of{\text{ }}dots{\text{ }}in{\text{ }}r{\text{ }}rows = r \times 9\]
\[ \Rightarrow number{\text{ }}of{\text{ }}dots{\text{ }}in{\text{ 8 }}rows = 8 \times 9 = 72\]
Number of dots in 10 rows is,
\[ \Rightarrow number{\text{ }}of{\text{ }}dots{\text{ }}in{\text{ }}r{\text{ }}rows = r \times 9\]
\[ \Rightarrow number{\text{ }}of{\text{ }}dots{\text{ }}in{\text{ 10 }}rows = 10 \times 9 = 90\]
So this completes Radhas’ rangoli!

Note:
This is not like a note but a dot rangoli is having either number of dots in a row and columns are the same. And it can also be drawn like this where the number of rows and columns are not the same. Don’t get confused here. We are not given any conditions so we will use the regular pattern like the same number of rows and columns.