/*! 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 59 The perimeter of a rectangle is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 59

The perimeter of a rectangle is y yards and \(f\) feet. What is the perimeter in inches?

Short Answer

Expert verified
The perimeter is \(36y + 12f\) inches.

Step by step solution

01

Convert yards to feet

Since there are 3 feet in a yard, multiply the number of yards (\(y\) ) by 3 to convert to feet.\[ ext{Total feet from yards} = 3 imes y \]
02

Add feet to total feet

Add the feet given in the problem (\(f\) feet) to the total feet from Step 1.\[ ext{Total feet} = 3y + f \]
03

Convert total feet to inches

Since there are 12 inches in a foot, multiply the total feet from Step 2 by 12 to convert to inches.\[ ext{Total inches} = 12 imes (3y + f) \]
04

Simplify the expression

Simplify the expression from Step 3 to find a clean expression that represents the perimeter in inches.\[ ext{Total inches} = 36y + 12f \]

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.

Perimeter Calculation
In geometry, calculating the perimeter involves finding the total length around a shape. For rectangles, the perimeter is calculated by adding up all the side lengths. If you have a rectangle's length and width, the formula to find the perimeter in feet is: \[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]If the dimensions are given in different units, such as yards and feet, you must first convert them into the same unit before calculating. This ensures that the perimeter is an accurate measurement of the entire length around the shape. Calculating perimeters is an essential skill in geometry, helping to understand the extents of shapes for various applications.
Arithmetic Operations
Arithmetic operations like addition, subtraction, multiplication, and division are the building blocks of math. When dealing with perimeter calculations and unit conversions, these operations are crucial. For instance, as seen in perimeter calculations, one frequently needs to
  • Add different measurements (like the original problem's feet and converted yardage).
  • Multiply measurements to convert units (like yards to feet or feet to inches).
Understanding how to perform these operations allows you to manipulate measurements confidently. This is why building a strong foundation in basic arithmetic is essential for solving any mathematical problem accurately.
Measurement Conversion
Measurement conversion involves changing from one unit to another, which is essential in many math problems to ensure consistency. In the exercise solution, various conversions are performed:
  • Converting yards to feet by multiplying by 3 (since 1 yard = 3 feet).
  • Converting feet to inches by multiplying by 12 (since 1 foot = 12 inches).
These conversions are done to express all measurements in a single unit, in this case, inches, making it easier to carry out calculations without unit discrepancies. Understanding how to convert units is crucial, especially in exercises that involve metric and imperial conversions, because accuracy in such conversions directly affects the correctness of the solution.

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

Perform the indicated operations. $$(-0.11)(-0.15)$$

Perform the indicated operations. $$14.36-5.89$$

Simplify each of the numerical expressions. $$0.34-0.21-0.74+0.19$$

Simplify each algebraic expression by combining similar terms. $$-2 x+1.7 x-4.6 x$$

Perform the indicated operations. $$-2.5+14.8$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Applied 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.