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What is the greatest possible straight-line distance, in centimeters,

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Math Expert
Joined: 02 Sep 2009
Posts: 52327
What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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04 Dec 2017, 22:03
00:00

Difficulty:

35% (medium)

Question Stats:

75% (00:59) correct 25% (01:12) wrong based on 20 sessions

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What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:

2017-12-05_0959_001.png [ 6.06 KiB | Viewed 1002 times ]

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Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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04 Dec 2017, 22:14
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

Bottom Plane to calculate the Hypotenuse
$$10^2 + 20^2 = 500$$
$$Hypo = 10\sqrt{5}$$

Plane parallel to Height
$$B = 10\sqrt{2}$$
$$Height = 10$$
$$Hypo = \sqrt{(100 + 500)} = 10\sqrt{6}$$
C
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Luckisnoexcuse

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Joined: 26 Oct 2017
Posts: 27
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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05 Dec 2017, 10:03
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

Is 20 cm correctly placed?

I feel like 20 cm and 10 cm are referring to same length

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Joined: 22 May 2016
Posts: 2353
What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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05 Dec 2017, 10:28
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

The longest straight-line distance in a right rectangular prism (a rectangular box) is between two opposite corners of the box.

If the measurements of the box are $$x, y, z$$, then the distance between two opposite corners, often called a "space diagonal," $$d$$, is

$$\sqrt{x^2 + y^2 + z^2}$$

Here, $$10^2 + 10^2 + 20^2 = d^2$$
$$600 = d^2$$
$$d = \sqrt{100 * 6} = 10\sqrt{6}$$

lesner19 , I agree, one measurement is mismarked. Whether you use one step or two to get the length of the space diagonal, though, the answer is the same because both depend on three distinct lengths.
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Joined: 25 May 2017
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Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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05 Dec 2017, 10:45
Formula for the diagonal of a rectangular box is always:

$$\sqrt{a^2+b^2+c^2}$$

Therefore it is just -

= $$\sqrt{10^2 + 10^2 + 20^2}$$

= $$\sqrt{100 + 100 + 400}$$

= $$\sqrt{600}$$

= 10$$\sqrt{6}$$
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Joined: 21 May 2013
Posts: 660
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:12
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52327
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:16
KS15 wrote:
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks

Yes, 10, 10 and 20 are width, breadth and length of the rectangle.
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Joined: 21 May 2013
Posts: 660
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:21
Bunuel wrote:
KS15 wrote:
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks

Yes, 10, 10 and 20 are width, breadth and length of the rectangle.

I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.
Math Expert
Joined: 02 Sep 2009
Posts: 52327
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:23
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.
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Joined: 21 May 2013
Posts: 660
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:28
Bunuel wrote:
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.

Well if it were clear, then 2 people would not be raising this point-Also, I wasted a few minutes trying to figure out how the width can be both 10 and 20-so it is certainly not obvious .
Math Expert
Joined: 02 Sep 2009
Posts: 52327
Re: What is the greatest possible straight-line distance, in centimeters,  [#permalink]

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15 Dec 2017, 01:30
KS15 wrote:
Bunuel wrote:
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.

Well if it were clear, then 2 people would not be raising this point-Also, I wasted a few minutes trying to figure out how the width can be both 10 and 20-so it is certainly not obvious .

Archived the question. Thank you very much for valuable input.

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This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: What is the greatest possible straight-line distance, in centimeters, &nbs [#permalink] 15 Dec 2017, 01:30
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