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A rectangular box is 10 inches wide, 10 inches long, and 5

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A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A) 15
(B) 20
(C) 25
(D) \(10\sqrt{2}\)
(E) \(10\sqrt{3}\)
[Reveal] Spoiler: OA
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Re: A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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New post 26 Dec 2012, 06:26
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Walkabout wrote:
A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A) 15
(B) 20
(C) 25
(D) \(10\sqrt{2}\)
(E) \(10\sqrt{3}\)


The longest distance will be the diagonal of a rectangular box. Look at the diagram below:
Image
Square of the diagonal of the face (base) is \(d^2=a^2+b^2\) and the square of the diagonal of a rectangular box is \(D^2=d^2+c^2=(a^2+b^2)+c^2\) --> \(D=\sqrt{a^2+b^2+c^2}\).

Applying this to our question, we get: \(D=\sqrt{10^2+10^2+5^2}=15\).

Answer: A.

Similar question to practice: a-rectangular-box-has-dimensions-of-8-feet-8-feet-and-z-128483.html
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Re: A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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New post 06 May 2014, 11:50
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One can also apply the 3-D or Deluxe Pythagorean theorem directly, which is D^2 = L^2 + W^2 + H^2, to get the value directly.
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Re: A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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Re: A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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New post 07 Jul 2016, 09:19
Walkabout wrote:
A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A) 15
(B) 20
(C) 25
(D) \(10\sqrt{2}\)
(E) \(10\sqrt{3}\)


To solve this problem we must remember that given any rectangular solid, the longest line segment that can be drawn within the solid will be one that goes from a corner of the solid, through the center of the solid, to the opposite corner, or in other words, the space diagonal of the solid.

The space diagonal can be calculated using the extended Pythagorean theorem:

diagonal^2 = length^2 + width^2 + height^2

Using the values from the given information we have:

d^2 = 10^2 + 10^2 + 5^2

d^2 = 100 + 100 + 25

d^2 = 225

√d^2 = √225

d = 15
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A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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New post 16 Jul 2016, 23:51
Walkabout wrote:
A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A) 15
(B) 20
(C) 25
(D) \(10\sqrt{2}\)
(E) \(10\sqrt{3}\)


The greatest distance between any two points in a CUBE/CUBOID is given by the formula
\(d=\sqrt{l^2+b^2+h^2}\)

\(d=\sqrt{100+100+25}\); \({given===> l=10; b=10; h=5}\)

\(d=\sqrt{225}= 15\)

Answer is A
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Re: A rectangular box is 10 inches wide, 10 inches long, and 5 [#permalink]

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New post 22 Sep 2016, 07:33
Hi I wonder if there is a faster way to solve this problem?

I read that if you find yourself using the Pythagorean theorem you missed a shortcut. Naturally I thought about triangles involving multiples of the following sides: 3,4,5 5,12,13 and 8,15,17. However none of these would suffice. Any other shortcuts?
Re: A rectangular box is 10 inches wide, 10 inches long, and 5   [#permalink] 22 Sep 2016, 07:33
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