In this question, it is given that two of the dimensions are 3 cm and 9 cm . Let the other dimension be x cm .
And the surface area of the rectangular prism is given. Now we use the formula of surface area of prism, which is
[tex] A = 2(length* width + width * height + length * height ) [/tex]
[tex] 198 = 2(3*9 + 3*x + 9*x) [/tex]
[tex] 99 = 27 + 12x [/tex]
Subtracting 27 to both sides,
[tex] 72 = 12x [/tex]
Dividing both sides by 12
[tex] x = 6 [/tex]
So the length of the remaining dimension is 6 cm .
