The perimeter of triangle PQR is 78, PQ=18, triangle PQR ~ triangle STU, AND ST=6. What is the perimeter of triangle STU?
This assumes that sides PQ and ST are corresponding sides. You do not state the relation of the sides in your problem.
Create a proportion matching the corresponding sides and perimeters.
PQ/ST = Perimeter PQR/Perimeter STU
18/6 = 78/x
18x = 468
x = 26 = Perimeter STU
17.3m
To find the perimeter of triangle STU, you need to use the fact that triangle PQR is similar to triangle STU. Similar triangles have proportional side lengths.
Given that PQ = 18 and ST = 6, you can set up a proportion between the corresponding side lengths:
PQ/ST = QR/TU
Substituting the given values:
18/6 = QR/TU
Simplifying the proportion:
3 = QR/TU
Now, you know that the ratio of the corresponding side lengths of the similar triangles is 3. To find the perimeter of triangle STU, you need to know the length of the sides TU and US.
Since you already know that ST = 6, you can multiply by the ratio to find the length of TU:
TU = 6 * 3 = 18
Similarly, you can find the length of US by multiplying ST by the ratio:
US = 6 * 3 = 18
Now that you have the lengths of all three sides of triangle STU:
ST = 6
TU = 18
US = 18
You can find the perimeter by adding all the side lengths:
Perimeter of triangle STU = ST + TU + US = 6 + 18 + 18 = 42
Therefore, the perimeter of triangle STU is 42.