Alright, let's break down the given problem step by step and find the complete solution.
Let's say Andrew wants to find the perimeter of a rectangular pen using the given expression. Assume the length of the pen ([tex]\( a \)[/tex]) is 10 meters, and we'll use the expression provided:
[tex]\[ \text{perimeter of pen} = 3a \][/tex]
### Step-by-Step Solution:
1. Understand the expression:
The expression for the perimeter is given as [tex]\( 3a \)[/tex]. Here, [tex]\( a \)[/tex] represents the length of the pen in meters.
2. Substitute the value:
Given that the length ([tex]\( a \)[/tex]) is 10 meters, substitute 10 for [tex]\( a \)[/tex] in the expression:
[tex]\[
\text{perimeter of pen} = 3 \times 10
\][/tex]
3. Calculate the result:
Perform the multiplication to find the perimeter:
[tex]\[
\text{perimeter of pen} = 30 \text{ meters}
\][/tex]
Thus, the perimeter of the pen, when the length is 10 meters, is 30 meters.
### Explanation using an example:
- If Andrew varies the length ([tex]\( a \)[/tex]), he can simply substitute different values of [tex]\( a \)[/tex] into the expression [tex]\( 3a \)[/tex] to find different perimeters.
- For instance, if [tex]\( a \)[/tex] were 5 meters, substituting into the same expression [tex]\( 3a \)[/tex]:
[tex]\[
\text{perimeter of pen} = 3 \times 5 = 15 \text{ meters}
\][/tex]
In summary, by substituting the given length into the expression [tex]\( 3a \)[/tex], Andrew can calculate the perimeter for any length of the pen. When [tex]\( a \)[/tex] is 10 meters, the perimeter is 30 meters.
