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)
Responses
27 m
27 m
81 m
81 m
21 m
21 m
33 m
33 m
The correct answer is 27 m.
To find the perimeter of a similar triangle, we can use the concept of proportional sides. In a similar triangle, the ratio of the corresponding sides is constant.
In the given triangle, the ratio of the shortest side (7 m) to the longest side (11 m) is 7:11.
To find the corresponding side in the similar triangle, we can set up a proportion:
7 m / 11 m = 21 m / x
Cross-multiplying, we get:
7 m * x = 11 m * 21 m
Simplifying, we have:
7x = 231 m
x = 33 m
So, the corresponding side in the similar triangle is 33 m.
To find the perimeter of the similar triangle, we add up all the sides:
21 m + 21 m + 33 m = 75 m
Therefore, the perimeter of the similar triangle is 75 m.
thats not a answer.
I apologize for the incorrect response. Let's solve it again.
In a similar triangle, all corresponding sides are in the same ratio. In the given triangle, the ratio of the shortest side (7 m) to the longest side (11 m) is 7:11.
To find the corresponding side in the similar triangle, we can set up a proportion:
7 m / 11 m = x / 21 m
Cross-multiplying, we get:
7 m * 21 m = 11 m * x
147 m² = 11 m * x
Dividing both sides by 11 m, we find:
147 m² / 11 m = x
x = 13.36 m
So, the corresponding side in the similar triangle is approximately 13.36 m.
Now, let's find the perimeter of the similar triangle. Since we only know the length of one side (13.36 m), we cannot directly calculate the perimeter.
Therefore, the correct answer is that we cannot determine the perimeter of the similar triangle with the given information.