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Answer :
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.
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.
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