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The greatest possible (straight line) distance, in inches, between any

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Math Expert
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The greatest possible (straight line) distance, in inches, between any [#permalink]

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07 Oct 2016, 01:33
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The greatest possible (straight line) distance, in inches, between any two points on a certain cube is 10. If the cube is modified so that its length is doubled and its width is doubled while its height remains unchanged, then what is the greatest possible (straight line) distance, in inches, between any two points on the modified box?

A. 10√2
B. 10√3
C. 20
D. 30
E. 30√3
[Reveal] Spoiler: OA

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The greatest possible (straight line) distance, in inches, between any [#permalink]

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07 Oct 2016, 04:35
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The greatest distance(straight line) between two points in a cube is its diagonal.
Here the length of the digaonal is 10.
Therefore, Side*$$\sqrt{3} = 10$$
Side = $$\frac{10}{\sqrt{3}}$$

Since the length and breadth doubles, and height remains the same.
The new box is a cuboid with length = breadth = $$\frac{20}{\sqrt{3}}$$ and height is $$\frac{10}{\sqrt{3}}$$

The straight line greatest distance is the diagonal.
Diagonal = $$\sqrt{length^2 + breadth^2 + height^2} = \sqrt{300} = 10*\sqrt{3}$$(Option B)
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Re: The greatest possible (straight line) distance, in inches, between any [#permalink]

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05 Jan 2018, 07:57
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Re: The greatest possible (straight line) distance, in inches, between any   [#permalink] 05 Jan 2018, 07:57
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