The sides of a triangle 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.
Let the sides of the similar triangle be a, b, and c, with a corresponding ratio k. We know that the ratio of corresponding sides in similar triangles is equal.
In this case, we have the following proportions:
a/7 = b/9 = c/11
a/21 = b/x = c/y
Cross multiplying the first proportion, we have:
7b = 9a
b = (9/7)a
Cross multiplying the second proportion, we have:
21b = x*a
b = (x/21)a
Setting them equal to each other, we have:
(9/7)a = (x/21)a
9/7 = x/21
x = (9/7)*21
x = 27
Therefore, the sides of the similar triangle are 21 m, 27 m, and 33 m.
To find the perimeter, we sum up the lengths of the sides:
Perimeter = 21 + 27 + 33 = 81 meters
The perimeter of the similar triangle is 81 meters.