To find the perimeter of a similar triangle, we simply multiply the lengths of each side of the original triangle by the same factor. Let's call this factor "x". In this case, we need to find the value of "x" that will give us a similar triangle with a shortest side length of 21 meters.
To find the value of "x", we can set up a proportion using the shortest side lengths:
7 m / 21 m = x / 21 m
Cross-multiplying, we get:
7 m * 21 m = 21 m * x
147 m^2 = 21 m * x
To isolate "x", we can divide both sides of the equation by 21 m:
147 m^2 / 21 m = x
7 m = x
Now that we have the value of "x", we can find the lengths of the other sides of the similar triangle by multiplying each side of the original triangle by 7:
Shortest side: 7 m * 7 = 49 m
Medium side: 9 m * 7 = 63 m
Longest side: 11 m * 7 = 77 m
The perimeter of the similar triangle is the sum of all three sides:
49 m + 63 m + 77 m = 189 m
Therefore, the perimeter of the similar triangle is 189 m. None of the given answer choices matches this result, so there may be a mistake in the problem or the choices provided.
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.
81 m
33 m
21 m
27 m
1 answer
1 answer