/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 A rectangle has a perimeter of 9... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 63

A rectangle has a perimeter of 9.5 inches. If the length is 2.75 inches, find the width.

Short Answer

Expert verified
The width of the rectangle is 2 inches.

Step by step solution

01

Understand the Formula for Perimeter

The perimeter of a rectangle is calculated using the formula: \( P = 2L + 2W \), where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width.
02

Plug in the Known Values

Substitute the given values for the perimeter and the length into the formula: \( 9.5 = 2(2.75) + 2W \).
03

Simplify the Equation

Calculate \( 2(2.75) \), which gives you \( 5.5 \). This simplifies the equation to: \( 9.5 = 5.5 + 2W \).
04

Solve for the Width

Subtract \( 5.5 \) from both sides of the equation to isolate the term with \( W \): \( 9.5 - 5.5 = 2W \), leading to \( 4 = 2W \).
05

Divide to Find the Width

Divide both sides by 2 to find \( W \): \( W = \frac{4}{2} \). This gives \( W = 2 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Solving Equations
Solving equations is a fundamental skill in mathematics that helps you find unknown values. In our exercise, we have the equation derived from the perimeter formula of a rectangle. Start by isolating the unknown, which is the width (\( W \)).
The equation given is simplified to \( 9.5 = 5.5 + 2W \).
  • First, perform the inverse operation to eliminate the known number from the side with the unknown. This means subtracting \( 5.5 \) from both sides.
  • Once simplified, you have \( 4 = 2W \).
  • To get \( W \) by itself, divide both sides by 2, which gives \( W = 2 \).
These steps show how equations are manipulated to solve for an unknown quantity.
Geometry Concepts
In geometry, understanding shapes and their properties is critical. A rectangle is a quadrilateral with opposite sides being equal and parallel. The rectangle's perimeter, which is the total distance around it, is given by the formula \( P = 2L + 2W \).
  • This formula comes from the sum of all sides: two lengths and two widths.
  • Recognizing these properties helps us apply our knowledge of formulas to find missing dimensions.
In our problem, knowing one dimension (length) and the perimeter, we apply geometric principles to find the width.
Prealgebra Problems
Prealgebra is a critical step in mathematics education where understanding the basic concepts of algebra starts. This includes working with simple equations and formulas.
The given problem is prealgebra in nature because it involves substituting values into a formula, simplifying, and solving for a variable.
  • Start with understanding the problem, breaking it down into smaller steps such as establishing what is known (the length and perimeter) and what is unknown (the width).
  • Using basic arithmetic operations, solve for the unknown by following a logical sequence.
Prealgebra problems like this prepare students for more advanced mathematical concepts by establishing a strong foundation in problem-solving and logical thinking.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Problems Work each of the following problems on your calculator. If rounding is necessary, round to the nearest hundred thousandth. $$0.0503 \div 0.0709$$

Carry out cach of the following divisions only so far as needed to round the results to the nearest hundredth. $$0.543 \div 2.1$$

Find each of the following sums and differences. (Add or subtract.) $$5 \frac{1}{10}+6 \frac{2}{100}+7 \frac{3}{1,000}$$

Write the fractions in order from smallest to largest. $$\frac{3}{8} \quad \frac{3}{16} \quad \frac{3}{4} \quad \frac{3}{10}$$

Reduce to lowest terms. $$\frac{15 x y}{30 x}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.