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If the box shown is a cube, then the difference in length be [#permalink]

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09 Aug 2009, 11:36

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If the box shown is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

Re: If the box pictured to the right is a cube, then the differe [#permalink]

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11 Aug 2009, 01:39

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lbsgmat wrote:

If the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C? 10% 20% 30% 40% 50%

main diagonal of a cube = bc = sqrt(3x^2) = xsqrt3 diagonal of a square = xsqrt2

difference = (sqrt 3 -sqrt 2)x = (1.7 - 1.4)x approx = 0.3x. distance A to C = x

If the box shown is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

A. 10% B. 20% C. 30% D. 40% E. 50%

AC is the edge (the side) of a cube, suppose it equals to 1; AB is the diagonal of a face, hence is equals to \(\sqrt{2}\), (either from 45-45-90 triangle properties or form Pythagorean theorem); BC is the diagonal of the cube itself and is equal to \(\sqrt{1^2+1^2+1^2}=\sqrt{3}\);