QuestionApril 14, 2026

5. What is the longest line segment that can be drawn in a right rectangular prism that is 21 cm wide, 28 cm long, and 15 cm high?

5. What is the longest line segment that can be drawn in a right rectangular prism that is 21 cm wide, 28 cm long, and 15 cm high?
5. What is the longest line segment that can be drawn in a right rectangular prism that is
21 cm wide, 28 cm long, and 15 cm high?

Solution
4.4(186 votes)

Answer

38.08 cm Explanation 1. Identify formula for space diagonal of a rectangular prism Longest line segment is the space diagonal: **d = \sqrt{l^2 + w^2 + h^2}**. 2. Plug in dimensions d = \sqrt{28^2 + 21^2 + 15^2} = \sqrt{784 + 441 + 225}. 3. Simplify d = \sqrt{1450}. 4. Approximate d \approx 38.0789 cm.

Explanation

1. Identify formula for space diagonal of a rectangular prism <br /> Longest line segment is the space diagonal: **$d = \sqrt{l^2 + w^2 + h^2}$**. <br />2. Plug in dimensions <br /> $d = \sqrt{28^2 + 21^2 + 15^2} = \sqrt{784 + 441 + 225}$. <br />3. Simplify <br /> $d = \sqrt{1450}$. <br />4. Approximate <br /> $d \approx 38.0789$ cm.
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