Question

A rectangular prism has a length of x+1, a width of 1/x+2 and a height of 5 cm. Find simplified expressions for the: a.) total surface area
b.) the lateral area

Answer 1

Let me get this straight\[l=x+1,~w=\frac{1}{x}+2,~h=5\]is that correct?

Answer 2

Even if it isn't, we can get going here. The total surface area is the lateral area plus the top and bottom. Lateral area (question b) is perimeter times height, which would work out to something like\[A_{lat}=h(2l+2w)=2h(l+w)\]Substitute to get a function of x. The area of the top and bottom area are lw, which gives the total area (question a) as\[A_{tot}=2[h(l+w)+lw]\]Again, substitution will give you the function in terms of x.

Answer 3

[p= 2(x=1)+2(1/x+2)\]
\[p=2x+2+2/x+2\]
\[p=2x(x+2)/x+2 + 2x(x+2)/x+2 + 2/x+2\]
\[p=2x^2+4x+2x+4+2/x+2\]

i'm not sure what to do next @AnimalAin

Answer 4

None of the formulas I showed you above is as complicated as what you have there. I am still not certain what the formula is for the width. Look at the formulas I put above, and substitute, then simplify.