A straw is placed inside a rectangular box that is 1 inches by 5 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
A straw is placed inside a rectangular box that is 1 inches by 5 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
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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![### Multistep Pythagorean Theorem (Level 2)
**Jun 01, 7:18:01 PM**
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**Problem Description:**
A straw is placed inside a rectangular box that is 1 inch by 5 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
**Diagram Explanation:**
- The problem includes a 3-dimensional rectangular prism (box) with the following dimensions:
- Length: 1 inch
- Width: 5 inches
- Height: 4 inches
- The diagram shows:
- A rectangular box drawn in perspective.
- A dashed line representing the diagonal of one of the faces.
- A solid line showing the diagonal from the bottom left corner of the front face to the top right back corner of the box.
To solve this problem, one can use the Pythagorean theorem in steps:
1. First, find the diagonal of the base rectangle using its length (1 inch) and width (5 inches):
\[ d_1 = \sqrt{(1^2 + 5^2)} = \sqrt{(1 + 25)} = \sqrt{26} \]
2. Then use \( d_1 \) and the height of the box to find the length of the straw:
\[
length_{straw} = \sqrt{(d_1^2 + height^2)} = \sqrt{(\sqrt{26}^2 + 4^2)} \]
\[
length_{straw} = \sqrt{(26 + 16)} = \sqrt{42} \]
Thus, the length of the straw, in simplest radical form, is \( \sqrt{42} \) inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc259b5f5-e220-45fd-9fc8-4087989c3f1a%2F1d9ede27-dfba-47e7-9872-c5b684c29e7e%2Fkw2uomx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Multistep Pythagorean Theorem (Level 2)
**Jun 01, 7:18:01 PM**
---
**Problem Description:**
A straw is placed inside a rectangular box that is 1 inch by 5 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
**Diagram Explanation:**
- The problem includes a 3-dimensional rectangular prism (box) with the following dimensions:
- Length: 1 inch
- Width: 5 inches
- Height: 4 inches
- The diagram shows:
- A rectangular box drawn in perspective.
- A dashed line representing the diagonal of one of the faces.
- A solid line showing the diagonal from the bottom left corner of the front face to the top right back corner of the box.
To solve this problem, one can use the Pythagorean theorem in steps:
1. First, find the diagonal of the base rectangle using its length (1 inch) and width (5 inches):
\[ d_1 = \sqrt{(1^2 + 5^2)} = \sqrt{(1 + 25)} = \sqrt{26} \]
2. Then use \( d_1 \) and the height of the box to find the length of the straw:
\[
length_{straw} = \sqrt{(d_1^2 + height^2)} = \sqrt{(\sqrt{26}^2 + 4^2)} \]
\[
length_{straw} = \sqrt{(26 + 16)} = \sqrt{42} \]
Thus, the length of the straw, in simplest radical form, is \( \sqrt{42} \) inches.
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