Rectangle Strip Length: A Math Problem

by TextBrain Team 39 views

Let's dive into a fun geometry problem involving a rectangular strip, equal parts, and multiples of a number. This is a cool question that combines basic arithmetic with a bit of spatial reasoning. So, grab your thinking caps, guys, and let’s get started!

Understanding the Problem

So, we've got this rectangular strip, right? Imagine a long piece of paper that's been neatly divided into smaller, equal sections. Each of these sections is 10 cm wide. Now, on each of these sections, we're writing down multiples of 17. But here’s the catch: we only want the multiples of 17 that are less than 200. And we're writing them in order, from the smallest to the biggest. The big question is: how long is the entire rectangular strip?

Keywords: Rectangular strip, equal parts, multiples of 17, length, geometry problem.

Breaking Down the Information

To solve this, we need to figure out a couple of things:

  1. What are the multiples of 17 that are less than 200? We need to list them out to see how many sections we're dealing with.
  2. How many sections are there in total? Each section represents one multiple of 17.
  3. What’s the total length of the strip? Since each section is 10 cm wide, we can multiply the number of sections by 10 to get the total length.

Finding the Multiples of 17

Okay, let's start by listing the multiples of 17 that are less than 200. We can do this by multiplying 17 by different whole numbers until we get a result greater than 200.

  • 17 x 1 = 17
  • 17 x 2 = 34
  • 17 x 3 = 51
  • 17 x 4 = 68
  • 17 x 5 = 85
  • 17 x 6 = 102
  • 17 x 7 = 119
  • 17 x 8 = 136
  • 17 x 9 = 153
  • 17 x 10 = 170
  • 17 x 11 = 187
  • 17 x 12 = 204

So, we stop at 17 x 11 because 17 x 12 exceeds 200. That means we have 11 multiples of 17 that fit our criteria: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, and 187.

Keywords: Multiples of 17, less than 200, listing multiples, arithmetic, problem-solving.

Calculating the Total Length

Now that we know there are 11 sections on the rectangular strip (each holding one of these multiples), and each section is 10 cm wide, we can easily calculate the total length.

Total length = Number of sections x Width of each section

Total length = 11 x 10 cm = 110 cm

Therefore, the length of the rectangular strip is 110 cm.

Keywords: Total length, number of sections, width, multiplication, calculation.

Putting It All Together

To recap, we started with a rectangular strip divided into equal parts. Each part was 10 cm wide, and we filled these parts with multiples of 17 that were less than 200. By listing out these multiples, we found that there were 11 such multiples. Since each multiple occupied a 10 cm section, the total length of the strip was simply 11 sections multiplied by 10 cm per section, giving us a final answer of 110 cm.

Visualizing the Solution

Imagine the rectangular strip. The first section has '17' written on it, the second has '34', the third has '51', and so on, all the way up to '187' on the eleventh section. Each of these sections is exactly 10 cm wide. If you were to take a ruler and measure the whole strip from the beginning of the first section to the end of the last section, you’d find it to be 110 cm long.

Why This Problem Matters

This problem isn't just about math; it's about problem-solving skills. It teaches you how to break down a complex problem into smaller, manageable steps. Here’s why it's useful:

  • Logical Thinking: You have to think logically about the conditions given (multiples of 17 less than 200) and how they relate to the physical dimensions of the strip.
  • Step-by-Step Approach: Breaking down the problem into finding the multiples, counting the sections, and then calculating the length helps develop a methodical approach to problem-solving.
  • Real-World Application: While this is a theoretical problem, it's easy to see how similar concepts apply to real-world situations, like measuring materials, planning layouts, or even organizing data.

Keywords: Problem-solving skills, logical thinking, step-by-step approach, real-world application, mathematical concepts.

Variations and Extensions

Want to make this problem even more interesting? Here are a few variations you can try:

  1. Change the Multiple: Instead of 17, use a different number. How does the length of the strip change if you use multiples of 13 or 23?
  2. Change the Limit: Instead of 200, set a different upper limit. What if you only consider multiples less than 150 or 250?
  3. Change the Width: What if the width of each section is different? How would you adjust your calculations if each section was 8 cm or 12 cm wide?
  4. Add a Condition: Add another condition, such as only considering even multiples or odd multiples. How does this affect the number of sections and the total length?

By playing around with these variations, you can deepen your understanding of the underlying concepts and sharpen your problem-solving abilities.

Keywords: Variations, extensions, problem variations, mathematical challenges, problem-solving skills.

Conclusion

So, there you have it! The length of the rectangular strip is 110 cm. This problem demonstrates how simple arithmetic and logical thinking can come together to solve a geometric puzzle. By breaking down the problem into smaller steps and carefully considering the information given, we were able to find the solution. Keep practicing these types of problems, and you'll become a math whiz in no time!

Remember, guys, math isn't just about numbers and formulas; it's about understanding the world around us. Problems like this one help us develop critical thinking skills that are useful in all areas of life. So keep exploring, keep questioning, and keep solving!

Keywords: Conclusion, problem-solving, arithmetic, logical thinking, geometry, mathematical puzzle.