To find the perimeter of a similar triangle where the shortest side is 21 meters, we first establish the ratio of the sides of the original triangle.
The sides of the original triangle are:
- 7 m (shortest)
- 9 m
- 11 m
The perimeter of the original triangle is: \[ 7 + 9 + 11 = 27 \text{ m} \]
Now, the shortest side of the similar triangle is given to be 21 m. The ratio of the similar triangle's shortest side to the original triangle's shortest side is: \[ \text{Ratio} = \frac{21 \text{ m}}{7 \text{ m}} = 3 \]
Since the triangles are similar, all corresponding sides are scaled by the same ratio of 3. Therefore, the lengths of the sides for the similar triangle will be:
- Shortest side: \( 21 \text{ m} \)
- Second side: \( 9 \text{ m} \times 3 = 27 \text{ m} \)
- Longest side: \( 11 \text{ m} \times 3 = 33 \text{ m} \)
Now, we compute the perimeter of the similar triangle: \[ 21 \text{ m} + 27 \text{ m} + 33 \text{ m} = 81 \text{ m} \]
Thus, the perimeter of the similar triangle is 81 m.