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? Choose the correct choice from the following answers: A) 10√2 B) 10√3 C) 20 D) 30 E) 30√3
The greatest distance(straight line) between two points in a cube is its diagonal.   Here the length of the digaonal is 10. Side*sqrt(3) = 10   Side = 10/sqrt(3)   Since the length and breadth doubles, and height remains the same.   The new box is a cuboid with length = breadth = 20/sqrt(3) and height is 10/sqrt(3)   The straight line greatest distance is the diagonal.   Diagonal = sqrt(length^2 + breadth^2 + height^2)   Diagonal = sqrt(300) = 10*sqrt(3)   Ans : (Option 10√3)
<result>B</result>
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?