To find the perimeter of a similar triangle where the shortest side has a length of 21 meters, we first need to identify the scaling factor based on the shortest side of the original triangle.
The shortest side of the original triangle is 7 m. The shortest side of the similar triangle is 21 m.
To find the scaling factor \( k \):
\[ k = \frac{\text{Shortest side of similar triangle}}{\text{Shortest side of original triangle}} = \frac{21}{7} = 3 \]
Now, we can find the lengths of the other sides of the similar triangle by multiplying the sides of the original triangle by this scaling factor:
- For the 9 m side: \[ 9 \times k = 9 \times 3 = 27 \text{ m} \]
- For the 11 m side: \[ 11 \times k = 11 \times 3 = 33 \text{ m} \]
Now, let's calculate the perimeter of the similar triangle:
\[ \text{Perimeter} = \text{Shortest side} + \text{Next side} + \text{Longest side} = 21 + 27 + 33 \]
Calculating it:
\[ 21 + 27 = 48 \] \[ 48 + 33 = 81 \text{ m} \]
Therefore, the perimeter of the similar triangle is 81 m.