Square Side Length Calculation: A Math Problem

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Hey guys! Let's dive into a cool math problem where we figure out the side length of a square. This problem involves a bit of cutting, measuring, and some geometry. So, grab your thinking caps, and let's get started!

Understanding the Problem

So, here's the deal: We've got a bar that's cut up into a bunch of equal pieces. To be exact, this bar is sliced vertically into 64 identical parts. Each of these parts is 25 cm long. Now, imagine we take all these little pieces and arrange them to form a perfect square. The question we need to answer is: How long is one side of that square?

This isn't just a straightforward measurement problem; it involves understanding how the total length of the pieces relates to the perimeter of the square and, ultimately, the length of its sides. We need to put on our problem-solving hats and break it down step by step. Think of it like a puzzle – we have all the pieces; we just need to arrange them in the right way to see the bigger picture. This kind of problem is fantastic for sharpening our math skills and getting us to think creatively. So, let's roll up our sleeves and figure this out!

Calculating the Total Length

Alright, the first thing we need to figure out is the total length of all those pieces we have. We know the bar was cut into 64 equal parts, and each part measures 25 cm. So, to find the total length, we just need to multiply these two numbers together. It’s like figuring out how much ribbon you have if you've got several pieces of the same length. In our case, we’re calculating the total length that will eventually form the perimeter of our square.

So, let’s do the math: 64 pieces multiplied by 25 cm per piece. This is a straightforward multiplication problem, but it’s a crucial step. The total length is the foundation for the rest of our calculations. Think of it as the raw material we have to work with. Without knowing the total length, we can’t figure out the size of the square we're going to make. Once we have this total, we can start thinking about how it translates into the sides of a square. So, let’s crunch those numbers and get ready for the next step in our geometric adventure! Remember, every step is important in solving a math problem, just like every piece is important in completing a puzzle.

Finding the Perimeter of the Square

Now that we know the total length of all the pieces, we're one step closer to solving our square-side mystery! Remember, we calculated the combined length of all 64 pieces, each measuring 25 cm. This total length is super important because it’s going to be the same as the perimeter of the square we form. Think about it: we're taking all those little lengths and arranging them to make the outline of a square. So, the total length of the pieces perfectly matches the distance around the square – that's the perimeter!

Understanding this connection is key. The perimeter is the sum of all the sides of a shape. For a square, that means adding up the lengths of its four equal sides. We've essentially transformed a linear measurement (the total length of the pieces) into a two-dimensional concept (the perimeter of a square). This is where geometry gets really interesting! Now that we know the perimeter, we're just one small step away from figuring out the length of a single side. It’s like we’re peeling back the layers of the problem, and the solution is getting closer and clearer. Let's keep going!

Calculating the Side Length

Okay, we've arrived at the final piece of the puzzle – calculating the side length of our square! We've already figured out the total length of all the pieces (64 pieces times 25 cm each) and understood that this total length is the same as the perimeter of the square we're forming. Now, we just need to use that information to find the length of one side.

Here’s the thing about squares: they have four sides, and all four sides are exactly the same length. This makes our job much easier! If we know the total distance around the square (the perimeter), we can simply divide that by the number of sides (which is 4) to find the length of one side. It’s like sharing a pie equally among four friends – each friend gets one-fourth of the pie. In our case, each side of the square gets one-fourth of the perimeter. So, we take the perimeter and divide it by 4. The result will be the length of a single side of the square, and that’s exactly what we’re looking for! This final calculation brings everything together, and we’ll have our answer in no time. Let’s do it!

Solution

Let's put it all together and solve this thing! We know:

  • The bar is cut into 64 pieces.
  • Each piece is 25 cm long.

First, we calculate the total length:

Total length = 64 pieces * 25 cm/piece = 1600 cm

This total length is the perimeter of our square. Now, to find the side length, we divide the perimeter by 4 (since a square has 4 equal sides):

Side length = Perimeter / 4 = 1600 cm / 4 = 400 cm

So, one side of the square is 400 cm. However, it seems there might be a mistake in the provided options (A) 24 B) 25 C) 28 D) 29, as none of them match our calculated answer. Let's re-examine the problem and our calculations to ensure accuracy.

Ah, I see the oversight! We correctly calculated the total length as 1600 cm and divided it by 4 to get 400 cm. However, the question is likely asking for the length of the side if the pieces themselves were arranged to form a square directly, not if the total length was used to form a square. Let's rethink our approach.

If we have 64 pieces, and we want to form a square, we need to think about how many pieces would make up each side. Since a square has 4 sides, we need to find a number that, when multiplied by itself, gets us close to 64. The square root of 64 is 8. So, we can arrange the 64 pieces into an 8x8 square.

Now, each side of the square is made up of 8 pieces, and each piece is 25 cm long. So, the side length of the square is:

Side length = 8 pieces * 25 cm/piece = 200 cm

Again, this doesn't match the provided options. It seems we need to consider another approach. Let's go back to the basics. The question states the pieces are used to form a square. This means the total length of all pieces forms the perimeter. We calculated the total length as 1600 cm. The perimeter of a square is 4 times the side length. So:

Perimeter = 4 * Side Length 1600 cm = 4 * Side Length Side Length = 1600 cm / 4 Side Length = 400 cm

It seems we keep arriving at 400 cm. Let's carefully review the options and the problem statement again. It's possible there's a typo in the options or a subtle detail we're missing.

Upon closer inspection, I realize we've made an incorrect assumption in interpreting how the pieces form the square. The key is that the total length of the 64 pieces forms the perimeter of the square. We correctly calculated the total length as 1600 cm. We then correctly divided this by 4 to find the side length, which is 400 cm. However, I missed a crucial step in relating the pieces directly to the square's formation.

Let's correct our interpretation: We have 64 pieces, each 25 cm long. To form a square, we need to arrange these pieces along the sides of the square. Let 's' be the number of pieces per side. Since a square has 4 sides, we have 4s pieces in total. So, 4s should equal 64. Solving for s:

4s = 64 s = 64 / 4 s = 16

This means there are 16 pieces per side. Each piece is 25 cm long, so the side length of the square is:

Side Length = 16 pieces * 25 cm/piece = 400 cm

We still arrive at 400 cm, which is not among the options. There might be an error in the question itself or the provided answers. However, let’s think differently. If we arrange the 64 pieces to make a filled square, not just the perimeter, then we arrange them in an 8x8 grid (since 8 * 8 = 64). Each piece is 25 cm, but this arrangement doesn't directly give us the side length of the square formed by the perimeter. We need to stick to the perimeter approach.

Given our calculations and the problem statement, the side length is indeed 400 cm. The options provided (A) 24 B) 25 C) 28 D) 29 seem to be incorrect. The correct approach is to calculate the total length and then divide by 4.

So, while we've solved the problem, the answer isn't in the options. It's a good reminder that sometimes, even in math, there can be errors in the questions themselves! Our process was sound, and we arrived at the logical answer based on the information given.

Conclusion

So, there you have it! We tackled a fun geometric problem, calculated the total length of the pieces, figured out the perimeter of the square, and finally, determined the length of one side. Even though our answer didn't match the given options, we learned a lot about problem-solving along the way. Remember, math is all about the journey, not just the destination. Keep those brains buzzing, and I'll catch you in the next math adventure! 🚀