Calculate The Cost Of Framing A Rectangular Painting

Hey guys! Let's dive into a fun and practical math problem that involves calculating the cost of framing a rectangular painting. This is something you might actually encounter in real life, whether you're an art enthusiast, an interior decorator, or just someone who loves a good DIY project. So, grab your thinking caps and let's get started!

Understanding the Problem

Okay, so here's the scenario: We have a rectangular painting that measures 80 centimeters by 60 centimeters. We want to put a frame around it, and this frame, including the labor cost of putting it together, costs 3 bolívares per decimeter. The big question is: How much will the entire frame cost us? To solve this, we need to break down the problem into smaller, more manageable steps. First, we'll figure out the perimeter of the painting, then we'll convert the measurements to decimeters, and finally, we'll calculate the total cost. Understanding the dimensions is crucial. The painting's dimensions of 80 cm by 60 cm give us a starting point for calculating the perimeter, which is the total length around the painting. This perimeter will directly translate into the length of the frame needed, and consequently, the cost. Remember, math problems are like puzzles; each piece of information is a clue that helps us find the solution. When you encounter a problem like this, always start by identifying what you know and what you need to find out. This will help you create a roadmap for solving the problem. This initial understanding is paramount because it sets the stage for the entire solution process. Without a clear grasp of the problem, any subsequent calculations might be misdirected. Think of it like building a house; you need a solid foundation before you can start constructing the walls and roof. Similarly, in math, understanding the problem is the foundation upon which you build your solution.

Calculating the Perimeter: The First Step

Let's talk about the perimeter, guys. The perimeter is the total distance around the outside of a shape. For a rectangle, it's like walking along all four sides and measuring the total distance you've walked. Remember the formula for the perimeter of a rectangle? It's simply twice the length plus twice the width. This is because a rectangle has two pairs of equal sides – two lengths and two widths. So, if our painting is 80 cm long and 60 cm wide, the perimeter is (2 * 80 cm) + (2 * 60 cm). Doing the math, that's 160 cm + 120 cm, which gives us a total perimeter of 280 cm. See? Not so scary, right? This is a fundamental step because the perimeter directly corresponds to the length of the frame we need. If we were to calculate the perimeter incorrectly, the entire cost calculation would be off. Think of it like measuring fabric for a sewing project; if you don't measure correctly, you might end up with a piece that's too short or too long. Similarly, in this problem, an accurate perimeter is essential for determining the correct frame length. Now, why is the perimeter so important in this context? Well, the frame needs to go all the way around the painting, so its length must match the perimeter. Each centimeter of the perimeter corresponds to a centimeter of the frame. Therefore, by calculating the perimeter, we're essentially figuring out how much material we need for the frame. This is a prime example of how geometry concepts like perimeter have practical applications in everyday situations. We're not just doing abstract math here; we're solving a real-world problem that involves framing a piece of art. So, let's take a moment to appreciate the connection between math and the world around us.

Converting Centimeters to Decimeters: Why It Matters

Now, here's a little twist! The cost of the frame is given in bolívares per decimeter, but our perimeter is in centimeters. Uh oh! We can't just multiply the perimeter in centimeters by the cost per decimeter; that would be like trying to mix apples and oranges. We need to make sure our units are consistent. So, how do we convert centimeters to decimeters? Remember that there are 10 centimeters in 1 decimeter. This is a key conversion factor that we'll use. To convert 280 cm to decimeters, we simply divide by 10. So, 280 cm / 10 = 28 dm. There you go! We've successfully converted our perimeter to the correct units. But why is this conversion so important? Well, it's all about ensuring that we're working with the same units of measurement. Imagine trying to measure the length of a room using inches for the width and feet for the length. It would be a confusing mess! Similarly, in this problem, if we didn't convert the perimeter to decimeters, we would end up with a completely incorrect cost calculation. This unit conversion is an essential step in problem-solving, especially in real-world applications where different units are often used. It's not just about getting the right number; it's about ensuring that the number represents the correct quantity in the appropriate units. In the realm of mathematics and its practical applications, consistency in units is not merely a matter of precision; it is a cornerstone of accuracy. Without uniformity in measurement, the results obtained become meaningless, akin to attempting to construct a building with mismatched blueprints. This underscores the importance of meticulously aligning units before engaging in any calculations, as even a seemingly minor discrepancy can cascade into significant errors. This principle extends beyond the confines of academic exercises and finds resonance in everyday scenarios, ranging from cooking recipes to home improvement projects. The ability to convert between units seamlessly is not just a mathematical skill; it is a practical tool that empowers us to navigate the complexities of the world with greater precision and confidence. Furthermore, the concept of unit conversion serves as a reminder that numbers, in and of themselves, do not possess inherent meaning. Their significance is derived from the context in which they are applied and the units they represent. A mere numerical value, devoid of its associated unit, is akin to a word stripped of its context, its true essence obscured. Thus, the adept manipulation of units is not merely a technicality but a fundamental aspect of mathematical literacy, enabling us to decipher the language of numbers and extract meaningful insights from the world around us. So, remember, always pay attention to the units! They're like the secret code that unlocks the solution.

Calculating the Total Cost: Putting It All Together

Alright, guys, we're in the home stretch now! We know the perimeter of the painting is 28 decimeters, and we know the frame costs 3 bolívares per decimeter. To find the total cost, we simply multiply the perimeter by the cost per decimeter. So, 28 dm * 3 bolívares/dm = 84 bolívares. Boom! We've got our answer. The frame will cost 84 bolívares. This final calculation is the culmination of all our previous efforts. It's where we bring together all the pieces of the puzzle to arrive at the solution. Each step we took – calculating the perimeter, converting units – was essential for this final calculation to be accurate. If we had made a mistake in any of the previous steps, it would have affected the total cost. This highlights the importance of careful and methodical problem-solving. It's not just about getting the right answer; it's about understanding the process and ensuring that each step is correct. Think of it like baking a cake; you can't just throw all the ingredients together and hope for the best. You need to follow the recipe carefully and measure everything accurately. Similarly, in math, each step is like an ingredient, and the final answer is like the finished cake. This final calculation also demonstrates the power of mathematical operations in solving real-world problems. Multiplication, in this case, is the key to finding the total cost. But it's not just about the operation itself; it's about understanding what the operation represents. Multiplication, in this context, is a shorthand way of adding the cost of each decimeter of the frame. We could have added 3 bolívares 28 times, but multiplication makes the process much more efficient. So, let's take a moment to appreciate the elegance and efficiency of mathematical tools in solving practical problems. And there you have it! We've successfully calculated the cost of framing a rectangular painting. We've tackled the problem step-by-step, from understanding the initial information to arriving at the final answer. This is a great example of how math can be used to solve everyday problems, and I hope you guys found it helpful and insightful.

Final Answer

The frame will cost 84 bolívares. Remember, math is all about breaking down problems into smaller, manageable steps and using the right tools to solve them.

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