Problem 5 - Basic Technical Mathematics with Calculus

Question

Find the perimeter of each figure. Square: side of \(85 \mathrm{m}\)

Step-by-Step Solution

Answer

The perimeter of the square is 340 meters.

Step 1: Identify Formula for Perimeter of a Square

The perimeter of a square can be found by using the formula \( P = 4s \), where \( s \) is the length of one side of the square. Since all sides of a square are equal, we multiply the side length by 4.

Step 2: Insert Given Side Length into Formula

You have a square with a side length of \( 85 \) meters. Insert this value into the formula: \( P = 4 imes 85 \).

Step 3: Calculate the Perimeter

Multiply the side length by 4 to find the perimeter: \( 4 imes 85 = 340 \).

Step 4: Provide the Answer with Units

The perimeter of the square is \( 340 \) meters.

Key Concepts

Understanding Geometry

Geometry is all about the study of shapes, sizes, and properties of different figures. When we talk about a square, we are referring to a special type of geometric shape: a quadrilateral with four right angles and four sides of equal length. This symmetry is what makes calculating the perimeter straightforward.

Understanding geometric principles like those of the square is essential because they form the foundation for many real-life applications. For instance, if you were planning to fence a square garden, you would need to know the perimeter to buy the correct amount of fencing material. Geometric concepts help us measure, compare, and interact with the world around us in a precise way.

Understanding the Mathematical Formula

The mathematical formula for determining the perimeter of a square is straightforward. A square, having equal sides, allows us to use a simple multiplication operation. The formula is \( P = 4s \), where \( s \) is the length of one side. This formula is a direct result of the definition of a square and its properties.

Why is this formula efficient? Because you're merely repeating the side length four times — one for each side of the square. This makes it extremely easy to remember and use. Additionally, it emphasizes the uniformity and equality present within the square's shape.

• Each side of the square equals the given length.
• All four sides contribute equally to the perimeter.

By plugging in the side length into this equation, you’ll quickly find how far you would need to travel to walk around the square once.

Simple Calculation Steps

To calculate the perimeter of a square, you only need to follow a few quick and simple steps. Imagine you have a square and you know each side is 85 meters long. Here’s how you find the perimeter.

**Begin by identifying the correct formula**, which as we've seen, is \( P = 4s \). This tells us that each length of the boundary contributes equally.

**Next, substitute the side length into the formula.** For this square, \( s = 85 \) meters. Plug this into the formula so it becomes \( P = 4 \times 85 \).

**Finally, perform the multiplication**. Calculate \( 4 \times 85 \), which is \( 340 \). Thus, the perimeter is 340 meters. This clear sequence ensures even complex problems can be handled with ease, providing a structured process for tackling geometry questions.