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.(1 point)
33 m
81 m
27 m
21 m
To find the perimeter of a similar triangle, we can use the concept of similarity ratios. The ratio of the corresponding sides of similar triangles is the same.
Let's denote the sides of the original triangle as a, b, and c: where a = 7m, b = 9m, and c = 11m.
Using the similarity ratio, we can set up the following proportion:
a / a' = b / b' = c / c'
where a', b', and c' are the corresponding sides of the similar triangle.
We are given that the shortest side of the similar triangle has a length of 21 meters. This means a' = 21m.
Plugging in the given values, we have:
7 / 21 = 9 / b' = 11 / c'
Solving for b':
7 / 21 = 9 / b'
Cross-multiplying:
7 * b' = 21 * 9
b' = (21 * 9) / 7
b' = 27
Similarly, for c':
7 / 21 = 11 / c'
Cross-multiplying:
7 * c' = 21 * 11
c' = (21 * 11) / 7
c' = 33
Therefore, the sides of the similar triangle are a' = 21m, b' = 27m, and c' = 33m.
To find the perimeter of the similar triangle, we sum up the lengths of the three sides:
Perimeter = a' + b' + c'
Perimeter = 21 + 27 + 33
Perimeter = 81 m
So, the perimeter of the similar triangle is 81 meters. Therefore, the correct answer is 81 m.