The Jock wrote:A cube has sides measuring 6 inches. What is the greatest possible (straight-line) distance, in inches, between any
two points on the box?
(A) 2underroot6
(B) 3underroot6
(C) 6underroot2
(D) 6underroot3
(E) 12
Not getting the exact picture how to get the answer. Please help
The greatest possible line that be drawn in a box is called
the main diagonal.
If l = length, w = width, h = height, and d = main diagonal, then use
the super-pythagorean theorem:
l^2 + w^2 + h^2 = d^2
In a cube, the length, width and height are the same, so if e = edge:
3(e^2) = d^2
In the problem above, e = 6, so:
3(6^2) = d^2
3(36) = d^2
108=d^2
d = sqrt(108) = sqrt(36 * 3) = sqrt(36) * sqrt(3) = 6sqrt(3)
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