Perimeter & Fencing: Triangle And Rectangle Calculations

Hey guys! Ever wondered how much fencing you need for your garden or how to calculate the perimeter of a rectangle? Let's dive into some cool math problems that deal with just that! We're going to tackle a triangular garden and a rectangle, figuring out perimeters and even how much wire you'd need for fencing. So, grab your calculators, and let's get started!

A Triangular Garden: Perimeter and Fencing

(i) Finding the Perimeter of the Garden

So, first off, we've got a garden shaped like a triangle. The sides of this triangular garden measure 20 cm, 25.5 cm, and a whopping 35.5 cm. Now, the perimeter – that's just the total distance around the outside, right? To calculate the perimeter of any shape, all we need to do is add up the lengths of all its sides. It’s like taking a walk around the edge of the garden; the total distance you walk is the perimeter.

In our case, we’ve got a triangle, which makes things pretty straightforward. We’ve got three sides, and we know the length of each one. To find the total perimeter, we simply add these lengths together. So, we’re looking at adding 20 cm, 25.5 cm, and 35.5 cm. This is a basic addition problem, but it’s super important in lots of real-world situations, like when you’re planning a fence or edging for your garden. Understanding how to calculate this helps you estimate materials and costs accurately.

Let's break down the addition step-by-step to make sure we get it right. First, we can add the whole numbers together, so 20 plus 25 equals 45. Then, we can add the decimal parts, 0.5 and 0.5, which gives us 1. Now, we add 45 and 35, which is 80. So far, we have 20 + 25.5 + 35.5 = 20 + 25 + 35 + 0.5 + 0.5. Continuing our calculation, we have 45 + 35 + 1 = 80 + 1. Finally, adding everything together, we get 81 cm. See how breaking it down into smaller steps makes it easier to manage? This kind of careful calculation is useful in many areas, not just in math class.

So, adding those up: 20 cm + 25.5 cm + 35.5 cm gets us a total of 81 cm. That means the perimeter of our triangular garden is 81 cm. Not too shabby, right? This is a crucial step because it tells us the total length we need to consider when we think about fencing or any other kind of border we might want to put around the garden. It's all about measuring and planning effectively.

(ii) Finding the Length of Wires Required for Fencing

Okay, so we know our garden's perimeter is 81 cm. Now, let's say we want to put a fence around it, not just once, but three times! This is where it gets a little trickier, but don't worry, we've got this. Fencing a garden helps protect it from animals, keeps those pesky critters out, and can even add a nice decorative touch. But how much wire do we actually need?

We're wrapping the fence around the garden three times, which means we need three times the length of the perimeter. Think of it like this: each round of wire needs to cover the entire perimeter, and we’re doing that three times. So, what we need to do is multiply our perimeter by 3. This is a straightforward multiplication problem, but it’s super practical. You use this kind of math all the time when you’re figuring out how much material you need for a project, whether it’s fencing, ribbon for a craft, or even ingredients for a recipe!

To calculate the total length of wire needed, we multiply the perimeter of the garden (81 cm) by the number of rounds (3). So, our calculation is 81 cm multiplied by 3. Let's do this multiplication step by step. First, we multiply 3 by 1, which gives us 3. Then, we multiply 3 by 8, which gives us 24. Combining these, we get 243. Therefore, 81 cm * 3 = 243 cm. Breaking it down like this makes it easier to see how the multiplication works and helps prevent mistakes. This approach is helpful in all sorts of calculations, making your math skills stronger and more reliable.

So, 81 cm multiplied by 3 is 243 cm. That means we need 243 cm of wire to fence our triangular garden with three rounds. Remember, this is the total length of wire we need, so it’s important to measure and cut accurately. It’s always a good idea to have a little extra, just in case! Understanding these calculations ensures you buy the right amount of materials and can complete your fencing project successfully. Isn’t it cool how math helps us in everyday tasks?

Rectangles: Calculating Perimeter

(i) Calculating the Perimeter of a Rectangle

Alright, let's switch gears from triangles to rectangles! This time, we're dealing with a rectangle that has a length (l) of 8.7 cm and a breadth (b) of 5.3 cm. Rectangles are everywhere – from books to doors to gardens – so knowing how to calculate their perimeters is super useful. The perimeter, as we know, is the total distance around the shape. But how do we find it for a rectangle?

The thing about rectangles is that they have two pairs of equal sides. That means there are two sides with the length l and two sides with the breadth b. To find the perimeter, we need to add up all these sides. A simple way to do this is to add the length and breadth together and then multiply the result by 2. This is because we have two lengths and two breadths. So, the formula for the perimeter (P) of a rectangle is P = 2 * (l + b). This formula is super handy and saves us time, especially when dealing with more complex problems.

In our case, the length (l) is 8.7 cm and the breadth (b) is 5.3 cm. We need to plug these values into our formula: P = 2 * (8.7 cm + 5.3 cm). Let's start by adding the length and breadth inside the parentheses. 8. 7 cm plus 5.3 cm equals 14 cm. Now, we have P = 2 * 14 cm. This is a simple multiplication problem: 2 multiplied by 14. To calculate this, we can think of it as adding 14 to itself, which gives us 28. So, the perimeter of our rectangle is 28 cm. This calculation is crucial for all sorts of projects, from framing a picture to building a tabletop. It’s all about understanding the properties of shapes and using them to solve real-world problems.

So, plugging in our values, we get P = 2 * (8.7 cm + 5.3 cm). First, we add 8.7 and 5.3, which equals 14 cm. Then, we multiply 14 cm by 2, which gives us 28 cm. So, the perimeter of our rectangle is 28 cm. See? Not too hard when you break it down! This kind of calculation is super practical, whether you're planning a garden, building a frame, or just trying to figure out how much ribbon you need to wrap a gift. Knowing these basics makes everyday tasks a whole lot easier.

Wrapping Up

And there you have it, guys! We’ve tackled finding the perimeter of a triangular garden, figured out how much fencing wire we need, and calculated the perimeter of a rectangle. These are all super useful skills, whether you're planning a real-life project or just flexing those math muscles. Remember, math isn't just about numbers; it's about solving problems and making sense of the world around us. Keep practicing, and you'll be perimeter pros in no time!