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
21 m
21 m
27 m
27 m
33 m
33 m
81 m
To find the perimeter of a similar triangle, we can use the property that corresponding sides of similar shapes are proportional.
In this case, we can set up a proportional relationship between the sides of the two triangles:
7/21 = 9/x = 11/y
To find the value of x, we can cross-multiply and solve for x:
7 * x = 21 * 9
x = (21 * 9) / 7
x = 27
Therefore, the length of the second side of the similar triangle is 27 meters.
To find the value of y, we can use the same approach:
9 * y = 21 * 11
y = (21 * 11) / 9
y ≈ 25.67
Therefore, the length of the third side of the similar triangle is approximately 25.67 meters.
Finally, we can calculate the perimeter of the similar triangle by adding up the lengths of all three sides:
21 + 27 + 25.67 ≈ 73.67
Therefore, the perimeter of the similar triangle is approximately 73.67 meters.
The correct answer is 33 m, 33 m.