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24 November, 04:17

The volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width. Find the length of the prism.

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Answers (1)
  1. 24 November, 04:56
    0
    Let the height of prism be

    H

    .

    As it is twice the width, width is

    H

    2

    .

    Length being

    3

    times width should be

    3

    *

    H

    2

    =

    3

    H

    2

    Hence, volume is

    3

    H

    2

    *

    H

    *

    H

    2

    =

    3

    4

    H

    3

    , but it is

    2058

    cubic cm.

    Therefore

    3

    4

    H

    3

    =

    2058

    and

    H

    3

    =

    2058

    *

    4

    3

    =

    686

    2058

    *

    4

    1

    3

    or

    H

    3

    =

    2

    *

    2

    *

    2

    *

    7

    *

    7

    *

    7

    Hence

    H

    =

    2

    *

    7

    =

    14

    Height of the prism is

    14

    cm.
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