Solving A Rectangle Perimeter Problem Finding Missing Sides

Hey guys! Ever find yourself scratching your head over a math problem that seems simple but has you stumped? Well, let's tackle one together! We've got a rectangle with a perimeter of 40 cm, and we know two of its sides are 10 cm each. The question is, how long are the other two sides? Don't worry; we'll break it down step by step so it's super easy to follow.

Understanding the Basics of Rectangles

Before we dive into solving this problem, let's quickly refresh our understanding of what a rectangle is and its key properties. A rectangle is a four-sided shape – a quadrilateral – where all four angles are right angles (90 degrees). This is super important because it means opposite sides are parallel and equal in length. Think of it like a neatly drawn picture frame or a perfectly rectangular book. These everyday objects help us visualize the shape we're dealing with.

Now, what about the perimeter? The perimeter is simply the total distance around the outside of the shape. Imagine you're walking around the rectangle; the total distance you walk is the perimeter. To calculate it, you add up the lengths of all four sides. This is a fundamental concept in geometry, and it's crucial for solving problems like the one we have at hand. Remember, the perimeter gives us a way to relate the lengths of all the sides, which is exactly what we need to find the missing lengths.

Understanding these basics—the properties of a rectangle and what the perimeter represents—is like having the right tools for a job. You wouldn't try to build a house without a hammer and nails, right? Similarly, we need these concepts to successfully solve our problem. So, keep these definitions in mind as we move forward. They're the foundation upon which we'll build our solution.

Setting Up the Equation for the Perimeter

Alright, now that we've got a good handle on what rectangles and perimeters are all about, let's get down to the nitty-gritty of setting up our equation. This is where we translate the words of the problem into a mathematical expression that we can actually solve. Remember, the key to any word problem is figuring out how to represent the information using symbols and numbers. So, let's see how it's done for this rectangle conundrum!

We know the perimeter of our rectangle is 40 cm. We also know that two sides are each 10 cm long. Let's call the length of the other two sides "x" because that's what we're trying to find. Since rectangles have two pairs of equal sides, both unknown sides will have the same length. Now, here's where the magic happens: we can express the perimeter as the sum of all the sides. Think of it like this: 10 cm (one side) + 10 cm (another side) + x (the third side) + x (the fourth side) equals the total perimeter.

So, our equation looks like this: 10 + 10 + x + x = 40. See how we've taken the information from the problem and turned it into a clear mathematical statement? This is a crucial step because it allows us to use algebra to find our answer. We've essentially created a map that will guide us to the solution. The equation is our roadmap, and each step we take in solving it brings us closer to our destination—the length of the missing sides.

Now, before we start crunching numbers, let's take a moment to appreciate the power of this equation. It's a compact way of representing all the information we have, and it sets us up for the next step: simplifying and solving for x. This is where the real fun begins!

Solving for the Unknown Sides

Okay, guys, now comes the exciting part where we actually solve for the unknown! We've set up our equation, 10 + 10 + x + x = 40, and now it's time to put our algebraic skills to the test. Don't worry; it's not as scary as it sounds! We'll take it one step at a time and make sure we understand each move.

The first thing we want to do is simplify our equation. This means combining like terms. We have two numbers (10 and 10) and two variables (x and x). So, let's add the numbers together: 10 + 10 = 20. And let's add the variables together: x + x = 2x. Now our equation looks much cleaner: 20 + 2x = 40.

See how much simpler that is? Now, we want to isolate the variable term (2x) on one side of the equation. To do this, we need to get rid of the 20. Remember, whatever we do to one side of the equation, we have to do to the other to keep things balanced. So, we subtract 20 from both sides: 20 + 2x - 20 = 40 - 20. This simplifies to 2x = 20.

We're almost there! Now we just need to get x by itself. The 2 is multiplying the x, so to undo that, we need to divide. We divide both sides of the equation by 2: (2x) / 2 = 20 / 2. This gives us x = 10.

And there you have it! We've solved for x. This means that the length of the other two sides of the rectangle is 10 cm each. High five! You've successfully navigated the algebraic waters and found the answer. Isn't it satisfying when a plan comes together? We started with a word problem, turned it into an equation, and then solved it step by step. That's the power of math in action!

Verifying the Solution

Before we celebrate our victory too enthusiastically, let's take a moment to verify our solution. It's always a good idea to double-check your work, especially in math. Think of it like proofreading a paper before you submit it. We want to make sure everything is correct and that our answer makes sense in the context of the original problem.

So, we found that the other two sides of the rectangle are 10 cm each. This means we have a rectangle with two sides that are 10 cm and another two sides that are also 10 cm. Let's plug these values back into our perimeter equation to see if it holds true. Remember, the perimeter is the sum of all the sides, so we add them up: 10 cm + 10 cm + 10 cm + 10 cm = ?

If we do the math, we get 40 cm. This is exactly what the problem told us the perimeter should be! So, our solution checks out. We've confirmed that our answer is correct and that our logic was sound. This gives us confidence that we've not only found the right answer but also understood the process along the way.

Verifying your solution is like putting the final piece in a puzzle. It completes the picture and gives you a sense of accomplishment. It also helps you solidify your understanding of the concepts involved. So, always take that extra step to verify, and you'll become an even more confident problem solver!

Conclusion: Math is Like a Puzzle

Alright, guys, we did it! We successfully solved the problem of finding the missing sides of a rectangle with a perimeter of 40 cm. We knew two sides were 10 cm each, and we figured out that the other two sides were also 10 cm each. This means we actually have a special kind of rectangle—a square! But more importantly, we walked through the process step by step, from understanding the basics of rectangles and perimeters to setting up an equation, solving for the unknown, and verifying our solution.

This whole exercise is a great example of how math can be like a puzzle. You're given some pieces of information, and you have to figure out how they fit together to solve the problem. It's like detective work! And just like any good puzzle, it's incredibly satisfying when you finally crack it.

So, the next time you encounter a math problem that seems daunting, remember this example. Break it down into smaller steps, use the tools and concepts you have learned, and don't be afraid to experiment. Math is not just about memorizing formulas; it's about problem-solving, critical thinking, and logical reasoning. And those are skills that will serve you well in all areas of life.

Keep practicing, keep exploring, and keep having fun with math! You've got this!