Sure, let's restate and solve the problem step-by-step.
Restatement of the Problem:
We need to determine how many matchsticks are required to construct 14 consecutive squares in a row, where each square shares sides with its neighboring squares.
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Step-by-Step Solution:
1. Understanding the Structure:
- For the first square, we need 4 matchsticks to form its four sides.
- For each additional square, because it shares one side with the previous square, you only need 3 additional matchsticks to form three new sides.
2. Breaking Down the Problem:
- For the very first square, we need 4 matchsticks.
- Each subsequent square requires 3 more matchsticks because it shares one side with the previous square.
3. Calculation:
- Let's calculate the total matchsticks required when we add these squares sequentially.
- The first square needs 4 matchsticks.
- Each of the next 13 squares (from 2nd to 14th) needs 3 matchsticks each.
4. Putting it Together:
- To find the total number of matchsticks, we sum up the matchsticks:
- Matchsticks for the first square: 4
- Matchsticks for each of the 13 additional squares: [tex]\(3 \times 13 = 39\)[/tex]
5. Summing the Total:
- Total matchsticks required = Matchsticks for the first square + Matchsticks for the additional squares
- Total matchsticks required = [tex]\(4 + 39 = 43\)[/tex]
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Conclusion:
Therefore, to construct 14 squares in a row, you would require a total of 43 matchsticks.
