Answer :
To solve this problem, we need to analyze the ages of the buildings and set up an inequality based on the given conditions. Let's break it down:
1. Understand the Problem:
- We have two buildings, B and D.
- Building B is built two years before Building D, which means Building B is 2 years older than Building D.
2. Define Variables:
- Let [tex]\( x \)[/tex] be the age of Building D.
- Since Building B is 2 years older, its age will be [tex]\( x + 2 \)[/tex].
3. Set Up the Inequality:
- We know the product of the ages of Buildings B and D should be at least 195. So, we need [tex]\( (x + 2) \times x \)[/tex] to be greater than or equal to 195.
4. Expression for the Product:
- The expression for this product is:
[tex]\[
x(x + 2) = x^2 + 2x
\][/tex]
- According to the problem, this needs to be at least 195:
[tex]\[
x^2 + 2x \geq 195
\][/tex]
Now, let's match this with the choices given:
- Option B mentions [tex]\( x^2 + 4x + 4 \geq 195 \)[/tex].
- The correct inequality we've derived is [tex]\( x^2 + 2x \geq 195 \)[/tex].
Therefore, from the analysis, it seems there isn’t a direct option that matches, but based on understanding the setup, the closest approach would be looking for the development pattern, although none of the original options fits precisely. Since none of the listed options are appropriate directly from the calculations provided, it suggests that there might have been a mismatch or a listing mistake. Check the options carefully if there's an error elsewhere in the problem.
1. Understand the Problem:
- We have two buildings, B and D.
- Building B is built two years before Building D, which means Building B is 2 years older than Building D.
2. Define Variables:
- Let [tex]\( x \)[/tex] be the age of Building D.
- Since Building B is 2 years older, its age will be [tex]\( x + 2 \)[/tex].
3. Set Up the Inequality:
- We know the product of the ages of Buildings B and D should be at least 195. So, we need [tex]\( (x + 2) \times x \)[/tex] to be greater than or equal to 195.
4. Expression for the Product:
- The expression for this product is:
[tex]\[
x(x + 2) = x^2 + 2x
\][/tex]
- According to the problem, this needs to be at least 195:
[tex]\[
x^2 + 2x \geq 195
\][/tex]
Now, let's match this with the choices given:
- Option B mentions [tex]\( x^2 + 4x + 4 \geq 195 \)[/tex].
- The correct inequality we've derived is [tex]\( x^2 + 2x \geq 195 \)[/tex].
Therefore, from the analysis, it seems there isn’t a direct option that matches, but based on understanding the setup, the closest approach would be looking for the development pattern, although none of the original options fits precisely. Since none of the listed options are appropriate directly from the calculations provided, it suggests that there might have been a mismatch or a listing mistake. Check the options carefully if there's an error elsewhere in the problem.
