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Lê Quốc Trần Anh Coordinator

15/11/2017 at 17:03
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A rectangular prism has dimensions in the ratio of 1:2:3. If the shortest edge is 2 ft, what is the longest distance between any two vertices? Express your answer as a decimal to the nearest hundredth.




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  • ...
    Phan Thanh Tinh Coordinator 15/11/2017 at 23:14

    A B C D A' B' C' D'

    Assume that CC' = 2 ft ; B'C' = 4 ft ; A'B' = 6 ft

    We see that A'C is the longest distance between any 2 vertices

    \(\Delta A'B'C'\) right at B' has : 

    \(A'C'^2=A'B'^2+B'C'^2=6^2+4^2=52\)

    \(\Delta A'C'C\) right at C' has :

    \(A'C=\sqrt{A'C'^2+CC'^2}=\sqrt{52+2^2}=\sqrt{56}\) (ft)

    So, the answer is : \(\sqrt{56}\approx7.48\) (ft)

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    Bảo Bình 15/11/2017 at 19:51

    The longest distance between any two vertices is:

               2:1 x 3=6(ft)=6 x 0,3048=1,8288\(\approx\)1,83(m)

    Answer:1,83 m

  • ...
    Nguyễn Hưng Phát 16/11/2017 at 12:36

    The longest distance between any two vertices is:

               2:1 x 3=6(ft)=6 x 0,3048=1,8288≈1,83 m

    Answer:1,83 m


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