Select the correct answer.

A construction company is analyzing which of its older projects need renovation. Building B was built two years before building C. Building D was built two years before building B. The product of building B's age and building D's age is at least 195. If [tex]x[/tex] represents the age of building C, which inequality represents this situation?

A. [tex]x^2 + 4 \geq 195[/tex]
B. [tex]x^2 + 8x + 16 \geq 195[/tex]
C. [tex]x^2 + 4x + 4 \geq 195[/tex]
D. [tex]x^2 + 6x + 8 \geq 195[/tex]

Let [tex]$x$[/tex] be the age of Building C.

1. Since Building B was built two years before Building C, the age of Building B is
[tex]$$x + 2.$$[/tex]

2. Building D was built two years before Building B, so its age is
[tex]$$(x + 2) + 2 = x + 4.$$[/tex]

3. The product of the ages of Building B and Building D is given by:
[tex]$$ (x + 2)(x + 4).$$[/tex]

4. We expand the product:
[tex]\[
(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
\][/tex]

5. According to the problem, the product is at least 195, so we set up the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195.
\][/tex]

6. Comparing this inequality with the given options, we see that it corresponds to option D.

Thus, the correct answer is option D.