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Chapter 3: Problem 10

Write the formula used to find the perimeter of a rectangle.

Short Answer

Expert verified
The formula for finding the perimeter of a rectangle is \(2*a + 2*b\), where 'a' and 'b' represent the lengths of the rectangle's sides.

Step by step solution

01

Identification of Rectangle Attributes

Identify the rectangle's properties. In a rectangle, opposite sides are equal. Thus, if one side is denoted as 'a' and another as 'b', the other sides will also be 'a' and 'b', respectively.
02

Establishment of Perimeter Definition

Understand the definition of perimeter. The perimeter of any shape is the sum of the lengths of its sides.
03

Formulation of Perimeter Formula

With this understanding, form the formula for the perimeter of a rectangle. Since there are two sides of length 'a' and two sides of length 'b', the sum will be 2*a + 2*b. This is the formula for the perimeter of a rectangle.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rectangle Attributes
When dealing with rectangles, it's important to know what defines this geometric shape. A rectangle is a flat, four-sided shape, with straight sides and right angles in every corner. The defining feature of a rectangle is that opposite sides are equal in length. This means that if you know the measurement of one side, you also know the measurement of its opposite side.
One pair of these equal sides can be referred to as 'length' (usually denoted as 'a'), while the other pair is often termed as 'width' (commonly denoted as 'b'). Knowing these attributes helps us understand how the perimeter and area of a rectangle can be calculated efficiently.
Rectangle Perimeter Formula
The perimeter of a rectangle is simply the total distance around the shape. To determine this, we need to consider the lengths of all four sides. As established in the rectangle attributes, opposite sides of a rectangle are equal. Therefore, if the length of the rectangle is 'a' and the width is 'b', the rectangle will have two sides each of length 'a' and two sides each of length 'b'.
The standard formula to find the perimeter (P) of a rectangle is:
  • \( P = 2a + 2b \)
Here, '2a' accounts for the two equal lengths, and '2b' accounts for the two equal widths. By plugging in the known measurements, you can calculate the total perimeter.
Understanding Perimeter
Perimeter is a fundamental concept in geometry, not just for rectangles but all shapes. It is essentially the total length of a shape鈥檚 boundary. Imagine walking around the edge of a rectangle; the distance you cover would be the perimeter.
Understanding perimeter is crucial for numerous real-world applications. For instance, when you need to put a fence around a rectangular garden, knowing the perimeter tells you how much fencing material you鈥檒l need. This concept extends beyond rectangles to include circles, triangles, and other polygons. Each shape has its own specific formula to calculate the perimeter.
Geometry for Beginners
Geometry lays the foundation for various mathematical concepts and is a part of many real-life applications. As a beginner, starting with basic shapes like rectangles is a great way to build your understanding. Recognizing the key properties and formulas associated with these shapes helps simplify more complex geometric problems later.
Learning geometry involves observation and practice. As you study various shapes, focus on their unique properties and how they relate to concepts like area and perimeter. Drawing shapes, measuring sides, and applying formulas are excellent ways to enhance your learning and confidence in this fascinating branch of mathematics.

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Most popular questions from this chapter

Express each sentence as a formula. The value \(v\) of a boat varies inversely with its age \(a\).

Express each variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. \(y\) varies jointly with \(x\) and \(w^{2} .\) If \(y=12\) when \(x=2\) and \(w=3,\) find \(y\) when \(x=3\) and \(w=2\).

Graph each equation by constructing a table of values and then plotting the points. SEE EXAMPLE 4 (OBJECTIVE 3) $$y-3=-\frac{1}{2}(2 x+4)$$

Graph each equation. SEE EXAMPLE 6. (OBJECTIVE 5 ) $$x=4$$

Set up a variation equation and solve for the requested value. For a fixed area, the length of a rectangle is inversely proportional to its width. A rectangle has a width of 8 feet and a length of 10 feet. If the length is increased to 16 feet, find the width of the rectangle.
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