Mathematics: Arectangular 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.

Arectangular prism (box) has a length of 21 m, a

drakkeo

11.01.2022

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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VictoriaRose520

29.06.2022

No. of Persons= 16

Step-by-step explanation:

There was a one phone line

Average no of people calling = 60 in one hour

% of all callers at most can get busy signal

Probability < 0.6

Probability for less than 1 person on hold = 0.2642

No of persons = 0.2642(60)

= 15.852 or 16

16 persons in hour the company is able to put on hold

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