Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Question
thumb_up100%
![**Determining the Diagonal Length of a City Block**
A standard city block is a square with each side measuring 101 yards. Find the length of the diagonal of a city block.
---
*Solution:*
To find the length of the diagonal of a square, we use the Pythagorean theorem. In a square, the diagonal forms two right-angled triangles.
The formula to calculate the diagonal (d) is:
\[ d = \sqrt{a^2 + a^2} \]
where \( a \) is the length of one side of the square.
For a city block with each side measuring 101 yards,
\[ d = \sqrt{101^2 + 101^2} \]
\[ d = \sqrt{2 \cdot 101^2} \]
\[ d = 101 \cdot \sqrt{2} \]
Using the approximate value of \( \sqrt{2} \approx 1.414 \),
\[ d \approx 101 \cdot 1.414 \]
\[ d \approx 142.814 \]
Therefore, the length of the diagonal is approximately 143 yards (rounded to the nearest whole number).
The length of the diagonal is approximately ___143___ yards.](https://content.bartleby.com/qna-images/question/a5da6b72-6f0b-4b5b-b99e-129f8d660be8/9f54d966-e509-4cdf-8d13-105f1ee7d5e0/fd51gg_processed.png)
Transcribed Image Text:**Determining the Diagonal Length of a City Block**
A standard city block is a square with each side measuring 101 yards. Find the length of the diagonal of a city block.
---
*Solution:*
To find the length of the diagonal of a square, we use the Pythagorean theorem. In a square, the diagonal forms two right-angled triangles.
The formula to calculate the diagonal (d) is:
\[ d = \sqrt{a^2 + a^2} \]
where \( a \) is the length of one side of the square.
For a city block with each side measuring 101 yards,
\[ d = \sqrt{101^2 + 101^2} \]
\[ d = \sqrt{2 \cdot 101^2} \]
\[ d = 101 \cdot \sqrt{2} \]
Using the approximate value of \( \sqrt{2} \approx 1.414 \),
\[ d \approx 101 \cdot 1.414 \]
\[ d \approx 142.814 \]
Therefore, the length of the diagonal is approximately 143 yards (rounded to the nearest whole number).
The length of the diagonal is approximately ___143___ yards.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 3 images
Knowledge Booster
Similar questions
- The perimeter of a rectangle is 14 cm. The width is 5 cm less than the lengh. Determine the dimensions of the rectangle. Simplifyarrow_forwardIn a rectangular park that measures 33 meters by 56 meters, a dog runs from one corner to the diagonally opposite corner. How far does the dog run?arrow_forwardA carpenter measures out 6 feet and 9 feet along the corner of a building. If the building is square how long should the diagonal measure? Expressing your answer as a radical:arrow_forward
- Mrs. Twining just bought a big-screen TV set. The diagonal of the screen is 55 inches. The TV is 27 inches tall. Calculate the perimeter of the TV.arrow_forwardIf the side of a square is 75 feet, find the perimeter of the square.arrow_forwardThe diagonal of a rectangular field is 104 feet. If the width of the field is 40 feet, what is the area of the field? 5 / 16arrow_forward
- Find the length of the missing leg of a right triangle if the hypotenuse measures 51 feet and the other leg measures 45 feetarrow_forwardMrs. Eaton is teaching a 5th grade class. She is standing 42 feet in front of Bill. Maura is sitting 40 feet to Bill's right. How far apart are Mrs. Eaton and Maura?arrow_forwardThe side of a regular decagon is 9 inches. Find the perimeter.arrow_forward
- A winter cover will be made for this swimming pool. The material for the cover sells for $2.50 per square metre. How many square metres are needed and how much will they cost? + 12 ft. 20 ft.arrow_forwardA football coach is blocking off a rectangular exercise area. The exercise area will have a perimeter of 76 yards. The length of one side will be 8 yards. How long will the other side be?arrow_forwardSolve. A picture frame is shaped like a rectangle whose perimeter is 280 cm.The length is 9 times as long as the width. Find the length and the width.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning 
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education