Class 9th Maths Ganita Manjari - Part I Chapter 2: Introduction to Linear Polynomials Exercise 7: End-Of-Chapter Exercises Question 12 (v) Solution

Question

Look at the first three stages of a growing pattern of hexagons made using matchsticks. A new hexagon gets added at every stage which shares a side with the last hexagon of the previous stage.

(v) Can 200 matchsticks form a stage in this pattern? Justify your answer.

Accepted Answer

Recall the expression derived in the previous question for the number of matchsticks in the $n$th stage.
 	ext{Matchstick count in the $n$th stage = $6 + 5(n - 1)$} Substitute $200$ for the matchstick count and solve for $n$.
 	ext{${color:#2E2EFF}200{/color} = 6 + 5(n - 1)$}|||	ext{marker{\Rightarrow} $200 = 6 + 5n - 5$}|||	ext{marker{\Rightarrow} $200 = 5n + 1$}|||	ext{marker{\Rightarrow} $5n = 200 - 1$}|||	ext{marker{\Rightarrow} $n = \dfrac{199}{5}$}|||	ext{marker{\Rightarrow} $n = 39.8$} Write the answer with a reason.
 {green}	extbf{Answer: No, 200 matchsticks cannot form a stage in this pattern.}|||	extbf{Reason: The value of $n$ must be a positive integer because it represents a stage number. Since $n = 39.8$ is not an integer, 200 matchsticks cannot form a stage in this pattern.}{/green}

Question: 12 (v)

Answer