A rectangular prism (box) has a length of 21 m, a width of 12 m, and a height of 16 m. Find the length of the greatest possible straight-lin

Question

A rectangular prism (box) has a length of 21 m, a width of 12 m, and a height of 16 m. Find the length of the greatest possible straight-line segment that can be contained in this box.

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Audrey 2 weeks 2021-09-12T07:55:09+00:00 1 Answer 0

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    2021-09-12T07:56:12+00:00

    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 \sqrt{l^{2}+b^{2} +h^{2}} units.

    Here, length is 21 m, width is 12 m and a height of 16 m.

    So, length of the diagonal is

    \sqrt{21^{2}+12^{2}+16^{2} } \\

    =\sqrt{441+144+256}

    =\sqrt{841}

    =29

    Hence, the length of the largest line-segment that can be contained in the box is 29 meters.

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