The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work. A. 6 inches width = w 30 inches
The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work. A. 6 inches width = w 30 inches
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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PLEASE HELP!!! The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work.
![**Problem A: Shipping Box Dimensions**
**Question:**
The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work.
**Diagram Description:**
The diagram shows a rectangular shipping box with a length of 30 inches, a height of 6 inches, and an unknown width labeled as \( w \). Inside the box, a bat is placed diagonally.
**Solution Explanation:**
To determine the width \( w \) required to fit a 36-inch bat in the box, the Pythagorean theorem can be used in three dimensions. The diagonal of the box must be at least 36 inches.
Given:
- Length, \( l = 30 \) inches
- Height, \( h = 6 \) inches
- Diagonal along the box \( d = 36 \) inches
We know the relationship for the diagonal \( d \) in a rectangular box:
\[ d = \sqrt{l^2 + h^2 + w^2} \]
Substituting the known values:
\[ 36 = \sqrt{30^2 + 6^2 + w^2} \]
Square both sides to eliminate the square root:
\[ 36^2 = 30^2 + 6^2 + w^2 \]
Calculate the squares:
\[ 1296 = 900 + 36 + w^2 \]
Combine like terms:
\[ 1296 = 936 + w^2 \]
Solve for \( w^2 \):
\[ w^2 = 1296 - 936 \]
\[ w^2 = 360 \]
Take the square root of both sides:
\[ w = \sqrt{360} \]
\[ w \approx 18.97 \]
So, the box should be approximately 19 inches wide to fit the 36-inch bat.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe35e825a-e1d1-4dd7-9e50-f66d167344ec%2F55ddac78-61e1-418c-91ea-c5688a3e9575%2F5m27h9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem A: Shipping Box Dimensions**
**Question:**
The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work.
**Diagram Description:**
The diagram shows a rectangular shipping box with a length of 30 inches, a height of 6 inches, and an unknown width labeled as \( w \). Inside the box, a bat is placed diagonally.
**Solution Explanation:**
To determine the width \( w \) required to fit a 36-inch bat in the box, the Pythagorean theorem can be used in three dimensions. The diagonal of the box must be at least 36 inches.
Given:
- Length, \( l = 30 \) inches
- Height, \( h = 6 \) inches
- Diagonal along the box \( d = 36 \) inches
We know the relationship for the diagonal \( d \) in a rectangular box:
\[ d = \sqrt{l^2 + h^2 + w^2} \]
Substituting the known values:
\[ 36 = \sqrt{30^2 + 6^2 + w^2} \]
Square both sides to eliminate the square root:
\[ 36^2 = 30^2 + 6^2 + w^2 \]
Calculate the squares:
\[ 1296 = 900 + 36 + w^2 \]
Combine like terms:
\[ 1296 = 936 + w^2 \]
Solve for \( w^2 \):
\[ w^2 = 1296 - 936 \]
\[ w^2 = 360 \]
Take the square root of both sides:
\[ w = \sqrt{360} \]
\[ w \approx 18.97 \]
So, the box should be approximately 19 inches wide to fit the 36-inch bat.
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