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Chapter 2: Problem 3

Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences. What formula cxpresses the perimeter of a rectangle in terms of length and width?

Short Answer

Expert verified
The formula for the perimeter of a rectangle is \( P = 2(l + w) \).

Step by step solution

01

Identify the components

First, identify the components of a rectangle. A rectangle has length (denoted as \( l \)) and width (denoted as \( w \)).
02

Understand the perimeter

Perimeter is the total distance around the edge of a shape. For a rectangle, this is the sum of all its sides.
03

Write the formula

Since a rectangle has two lengths and two widths, the formula for the perimeter \( P \) can be expressed as: \[ P = 2l + 2w \] This can also be simplified to: \[ P = 2(l + w) \]

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Key Concepts

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

Length and Width
When dealing with rectangles, the two main dimensions you need to know are length and width.
The **length** of a rectangle is the longer side, while the **width** is the shorter side.
These measurements are fundamental in various calculations involving rectangles, such as finding the perimeter or area.

Understanding these dimensions is crucial because they define the overall size and shape of the rectangle.
Always denote length as **l** and width as **w** in mathematical formulas.
Knowing the correct identification and notation helps you apply the formulas accurately in solving geometry problems.
Perimeter Calculation
The **perimeter** of a rectangle is the total distance around its edges.
To calculate the perimeter, add up the lengths of all four sides.

However, since a rectangle has two pairs of equal sides, you can simplify this calculation.
The formula to find the perimeter **P** of a rectangle in terms of length **l** and width **w** is:



P = 2l + 2w

Alternatively, you can also write the formula as:

P = 2(l + w)

Using this formula is efficient and straightforward, making perimeter calculations quick and easy.
Geometry Basics
In geometry, understanding basic shapes and their properties is essential.
A **rectangle** is a four-sided shape with opposite sides that are equal in length and all interior angles are right angles (90 degrees).
This makes it a type of quadrilateral that's easy to work with in calculations.

**Key properties of rectangles** include:
  • Opposite sides are of equal length.
  • All angles are right angles.
  • Diagonals bisect each other and are equal in length.

Familiarizing yourself with these properties helps in accurately solving problems involving rectangles.
This foundational knowledge is crucial as many more complex geometric concepts build upon these basics.
Always start with identifying the shape properties before applying relevant formulas.

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Most popular questions from this chapter

Solve each problem by using an absolute value equation or inequality. See Example 10. Famous battles. In the Hundred Years鈥橶ar, Henry V defeated a French army in the battle of Agincourt and Joan of Arc defeated an English army in the battle of Orleans (The Doubleday Almanac). Suppose you know only that these two famous battles were 14 years apart and that the battle of Agincourt occurred in 1415. Use an absolute value equation to find the possibilities for the year in which the battle of Orleans occurred.

Show a complete solution to each problem. Increasing the percentage. A mechanic has found that a car with a 16 -quart radiator has a \(40 \%\) antifreeze mixture in the radiator. She has on hand a \(70 \%\) antifreeze solution. How much of the \(40 \%\) solution would she have to replace with the \(70 \%\) solution to get the solution in the radiator up to \(50 \% ?\)

Solve each problem. Nicholas is painting black squares of various sizes on one white wall of his living room. The first square has 1 -in. sides, the second has 2 -in. sides, the third has 3-in. sides, and so on. If he does 40 squares, then how much area (in square feet) will they cover? The formula \(S=\frac{n(n+1)(2 n+1)}{6}\) gives the sum of the squares of the integers from 1 through \(n .\) Will all of these squares fit on an 8 -foot by 15 -foot wall?

Solve each equation. $$-3.48 x+6.981=4.329 x-6.851$$

If 3 is added to every number in \((4, \infty),\) the resulting set is \((7, \infty) .\) In each of the following cases, write the resulting set of numbers in interval notation. Explain your results. a) The number \(-6\) is subtracted from every number in \([2, \infty)\) b) Every number in \((-\infty,-3)\) is multiplied by 2 c) Every number in \((8, \infty)\) is divided by 4 d) Every number in \((6, \infty)\) is multiplied by \(-2\) e) Every number in \((-\infty,-10)\) is divided by \(-5\)
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