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7. Jason has a trunk whose inside is 16 inches wide, 30 inches long and 12 inches high. Will a telescope measuring 34 inches fit in the trunk with the lid closed?

7. Jason has a trunk whose inside is 16 inches wide, 30 inches long and 12 inches high. Will a telescope measuring 34 inches fit in the trunk with the lid closed?

Elementary Geometry For College Students, 7e
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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**Problem 7:** Jason has a trunk whose inside dimensions are 16 inches wide, 30 inches long, and 12 inches high. Will a telescope measuring 34 inches fit in the trunk with the lid closed? **Explanation:** To determine if the telescope can fit inside the trunk, we must consider not only the dimensions of the trunk but also the diagonal length of the trunk, as this will indicate the maximum length of an item that can be accommodated. **Step-by-step solution:** 1. **Calculate the diagonal of the base** (rectangle of width and length): - Use the Pythagorean theorem: \( \text{Diagonal} = \sqrt{(16^2 + 30^2)} \) 2. **Calculate the diagonal of the rectangular prism (trunk)**: - Use the three-dimensional distance formula: \( \text{Diagonal} = \sqrt{(16^2 + 30^2 + 12^2)} \) Compare this diagonal length to the length of the telescope (34 inches) to determine if the telescope can fit inside the trunk. This approach illustrates the importance of spatial understanding and application of the Pythagorean theorem in three dimensions.
Transcribed Image Text:**Problem 7:** Jason has a trunk whose inside dimensions are 16 inches wide, 30 inches long, and 12 inches high. Will a telescope measuring 34 inches fit in the trunk with the lid closed? **Explanation:** To determine if the telescope can fit inside the trunk, we must consider not only the dimensions of the trunk but also the diagonal length of the trunk, as this will indicate the maximum length of an item that can be accommodated. **Step-by-step solution:** 1. **Calculate the diagonal of the base** (rectangle of width and length): - Use the Pythagorean theorem: \( \text{Diagonal} = \sqrt{(16^2 + 30^2)} \) 2. **Calculate the diagonal of the rectangular prism (trunk)**: - Use the three-dimensional distance formula: \( \text{Diagonal} = \sqrt{(16^2 + 30^2 + 12^2)} \) Compare this diagonal length to the length of the telescope (34 inches) to determine if the telescope can fit inside the trunk. This approach illustrates the importance of spatial understanding and application of the Pythagorean theorem in three dimensions.
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