find the rule which gives the number of matchsticks required to make following motchsticks pattern use a variable to write the rule a pattern of letter h an y

To determine the number of matchsticks required to create the patterns of the letters "h" and "y," we can analyze each letter's structure and derive a mathematical rule based on the number of segments used in each letter. Let's break this down step by step.

Understanding the Structure of the Letters

Both letters consist of straight lines that can be represented by matchsticks. Here’s how each letter is formed:

Letter "h"

• The letter "h" consists of two vertical matchsticks and one horizontal matchstick connecting the two verticals in the middle.
• Thus, the total number of matchsticks for "h" can be calculated as follows:

Matchsticks for "h": 2 (vertical) + 1 (horizontal) = 3 matchsticks

Letter "y"

• The letter "y" has two diagonal matchsticks forming the upper part and one vertical matchstick for the lower part.
• So, the total number of matchsticks for "y" is:

Matchsticks for "y": 2 (diagonal) + 1 (vertical) = 3 matchsticks

Formulating the Rule

Now that we have analyzed both letters, we can summarize the findings. Each letter requires a total of 3 matchsticks. If we denote the number of letters as a variable, say N, the total number of matchsticks required for N letters can be expressed with a simple rule:

Rule: Total matchsticks = 3 * N

Examples of Applying the Rule

Let’s apply this rule to find out how many matchsticks are needed for different numbers of letters:

• If N = 1 (one letter, either "h" or "y"):
  Total matchsticks = 3 * 1 = 3
• If N = 2 (two letters, "h" and "y"):
  Total matchsticks = 3 * 2 = 6
• If N = 5 (five letters, any combination of "h" and "y"):
  Total matchsticks = 3 * 5 = 15

Visualizing the Patterns

To better understand, you can visualize the letters as follows:

• For "h": Imagine two vertical lines with a horizontal line connecting them in the middle.
• For "y": Picture two diagonal lines meeting at a point above a vertical line.

This visualization reinforces how each letter is constructed from matchsticks, leading to our derived rule. By applying this logic, you can calculate the number of matchsticks needed for any combination of the letters "h" and "y." This approach not only helps in understanding the patterns but also enhances your problem-solving skills in mathematics.