Question

The length of a rectangular prism is half the height. The width is one-third the length. The height is 12 cm. What are the dimensions and surface area of the rectangular prism?

Answer 1

Dimensions: `12 xx 6 xx 2` cm.
Surface area: `216` sq.cm.

Explanation:

Using `H` for height; `W` for width; and `L` for length (all in cm.):

Dimensions
We are told
`color(white)("XXX")L=1/2H`
`color(white)("XXX")W=1/3L`
`color(white)("XXX")H=12`

`L=1/2H=1/2xx12=6`

`W=1/3L=1/3xx6=2`

Surface Area
Surface Area `= 2xx(WxxH + LxxH + LxxW)`

`color(white)("XXXXXXX")=2xx(24+72+12)`

`color(white)("XXXXXXX")=2xx(108)`

`color(white)("XXXXXXX")=216`