Answer:
29 meters
Step-by-step explanation:
Given: A rectangular prism (box) has a length of 21 m, a width of 12 m, and a height of 16 m.
To find: The length of the greatest possible straight-line segment that can be contained in this box.
Solution: In a rectangular prism(box), the largest length of the greatest possible line segment is the diagonal of the prism.
Now, we know that if l, b, and h are the length, width and height of the prism.
The diagonal of the prism is [tex]\sqrt{l^{2}+b^{2} +h^{2}}[/tex] units.
Here, length is 21 m, width is 12 m and a height of 16 m.
So, length of the diagonal is
[tex]\sqrt{21^{2}+12^{2}+16^{2} } \\[/tex]
[tex]=\sqrt{441+144+256}[/tex]
[tex]=\sqrt{841}[/tex]
[tex]=29[/tex]
Hence, the length of the largest line-segment that can be contained in the box is 29 meters.
