A standard city block is a square with each side measuring 101 yards. Find the length of the diagonal of a city block. The length of the diagonal is approximately yards.
A standard city block is a square with each side measuring 101 yards. Find the length of the diagonal of a city block. The length of the diagonal is approximately yards.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**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.
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*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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5da6b72-6f0b-4b5b-b99e-129f8d660be8%2F9f54d966-e509-4cdf-8d13-105f1ee7d5e0%2Ffd51gg_processed.png&w=3840&q=75)
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.
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