Question

The rectangular prism is shown below the surface area of each faces label which values represent the dimensions in centimeters of the rectangular prism

A. 12, 18, 24
B. 3, 4, 8
C. 3, 4, 6
D. 2, 9, 12
​

Answer 1

A. 3, 4, 6

Explanation:

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. On the other hand, a rectangular prism is a solid whose base is a rectangle. The surface area of a solid is the total area of its outer surface. For a rectangular prism, we have three characteristic sides, which are height, width and depth. If:

`height=a \\ \\ width=b \\ \\ depth=c`

Then, from the figure below we have:

`(1) \ a* b=24 \\ \\ (2) \ a* c=18 \\ \\ (3) \ b* c=12 \\ \\ \\ From \ 1 \ and \ 3: \\ \\ b=(24)/(a)=(12)/(c) \therefore 24c=12a \ (4) \\ \\ From \ 2: \\ \\ a=(18)/(c) \\ \\ 2 \ into \ 4: \\ \\ 24c=12* (18)/(c) \therefore c^2=9 \therefore \boxed{c=3} \\ \\ \\ c \ into \ 2: \\ \\ a=(18)/(3) \therefore \boxed{a=6} \\ \\ \\ c \ into \ 3: \\ \\ b=(12)/(3) \therefore \boxed{b=4}`

Finally, the dimensions are:

3, 4 and 6 cm