Answer :
Let [tex]$x$[/tex] represent the age of building [tex]$C$[/tex]. According to the problem:
1. Building [tex]$B$[/tex] was built two years before building [tex]$C$[/tex], so its age is [tex]$x+2$[/tex].
2. Building [tex]$D$[/tex] was built two years before building [tex]$B$[/tex], so its age is [tex]$x+4$[/tex].
The product of the ages of buildings [tex]$B$[/tex] and [tex]$D$[/tex] is given by
[tex]$$
(x+2)(x+4).
$$[/tex]
Expanding this product:
[tex]$$
(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
$$[/tex]
The problem states that the product of the ages is at least [tex]$195$[/tex]:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
This inequality matches option A.
1. Building [tex]$B$[/tex] was built two years before building [tex]$C$[/tex], so its age is [tex]$x+2$[/tex].
2. Building [tex]$D$[/tex] was built two years before building [tex]$B$[/tex], so its age is [tex]$x+4$[/tex].
The product of the ages of buildings [tex]$B$[/tex] and [tex]$D$[/tex] is given by
[tex]$$
(x+2)(x+4).
$$[/tex]
Expanding this product:
[tex]$$
(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
$$[/tex]
The problem states that the product of the ages is at least [tex]$195$[/tex]:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
This inequality matches option A.