**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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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.

---

*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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