Answer:
A. 3, 4, 6
Step-by-step 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:
[tex]height=a \\ \\ width=b \\ \\ depth=c[/tex]
Then, from the figure below we have:
[tex](1) \ a\times b=24 \\ \\ (2) \ a\times c=18 \\ \\ (3) \ b\times c=12 \\ \\ \\ From \ 1 \ and \ 3: \\ \\ b=\frac{24}{a}=\frac{12}{c} \therefore 24c=12a \ (4) \\ \\ From \ 2: \\ \\ a=\frac{18}{c} \\ \\ 2 \ into \ 4: \\ \\ 24c=12\times \frac{18}{c} \therefore c^2=9 \therefore \boxed{c=3} \\ \\ \\ c \ into \ 2: \\ \\ a=\frac{18}{3} \therefore \boxed{a=6} \\ \\ \\ c \ into \ 3: \\ \\ b=\frac{12}{3} \therefore \boxed{b=4}[/tex]
Finally, the dimensions are:
3, 4 and 6 cm
