The sides of a triangular path measure 7 m, 9 m, and 11 m. Find the perimeter of a similar triangle in which the shortest side has a length of 21 meters.
27 m
27 m
81 m
81 m
21 m
21 m
33 m
We can solve this problem using the concept of similarity in triangles.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
In this case, the triangles are similar because their corresponding angles are equal (both have the same angles) and their corresponding sides are in proportion.
To find the perimeter of the similar triangle, we need to find the other two sides of the triangle.
Since the shortest side of the original triangle measures 7m and the corresponding side in the similar triangle measures 21m, we can set up the following proportion:
7/21 = 9/x
Cross-multiplying, we get:
7x = 9 * 21
7x = 189
x = 189/7
x = 27
So, the other side of the similar triangle measures 27m.
Similarly, we can find the third side of the similar triangle:
7/21 = 11/y
Cross-multiplying, we get:
7y = 11 * 21
7y = 231
y = 231/7
y = 33
So, the third side of the similar triangle measures 33m.
The perimeter of the similar triangle is the sum of its sides:
21 + 27 + 33 = 81m.
Therefore, the correct answer is 81 m.