Select the correct answer.
An online retailer is shipping a shower curtain pole that is 13 feet long. Their largest box is in the shape of a rectangular prism that is . Will the pole fit in the box?

A.
No, because the longest diagonal of the box is 12.1 feet long.
B.
Yes, because the longest diagonal of the box is 15.7 feet long.
C.
Yes, because the longest diagonal of the box is 13.5 feet long.
D.
No, because the longest diagonal of the box is 12.8 feet long.

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MrRoyal MrRoyal · Answer 1 · 2022-02-02T20:06:48+01:00

The rectangular prism will fit in the pole if the longest diagonal in the pole is less than 13 feet.

The longest diagonal (d) in the prism is calculated using;

[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]

Where x, y and z are the dimensions of the prism.

Assume the dimensions are: 4, 5 and 6 feet,

The formula becomes

[tex]d = \sqrt{4^2 + 5^2 + 6^2[/tex]

[tex]d = \sqrt{77[/tex]

[tex]d = 8.8[/tex]

Using the assumed dimensions, the rectangular prism will fit in the pole if the longest diagonal.

This is so because: 8.8 feet is less than 13 feet