To find the perimeter of a similar triangle when the shortest side measures 21 meters, we first need to determine the ratio of similarity between the triangles.
The shortest side of the original triangle is 7 meters, and the shortest side of the similar triangle is 21 meters.
The ratio of the sides is given by:
\[ \text{Ratio} = \frac{\text{Shorter side of similar triangle}}{\text{Shorter side of original triangle}} = \frac{21 \text{ m}}{7 \text{ m}} = 3 \]
In a similar triangle, all sides are scaled by the same ratio. Therefore, we can find the lengths of the other two sides of the similar triangle:
- The second side (originally 9 m):
\[ 9 \text{ m} \times 3 = 27 \text{ m} \]
- The third side (originally 11 m):
\[ 11 \text{ m} \times 3 = 33 \text{ m} \]
Now, we can find the perimeter of the similar triangle by adding all the sides together:
\[ \text{Perimeter} = 21 \text{ m} + 27 \text{ m} + 33 \text{ m} = 81 \text{ m} \]
Thus, the perimeter of the similar triangle is 81 m.