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.

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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step-by-step explanation:

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