Question

Triangles ABC and TUV are similar. The length of the sides of ABC are 40, 50, and 24. The length of the longest side of TUV is 275. Using what you have learned about similar triangles, find the perimeter of TUV. Show your calculations.

a) 330 units
b) 440 units
c) 550 units
d) 660 units

Answer 1

To find the perimeter of TUV, we use the concept of similar triangles and the scale factor determined by the longest sides. The perimeter of TUV is 627 units.

Step-by-step explanation:

Since triangles ABC and TUV are similar triangles, we can use the concept of corresponding sides to find the perimeter of TUV. The longest side of ABC corresponds to the longest side of TUV. Let's find the scale factor by dividing the length of the longest side of TUV (275 units) by the length of the longest side of ABC (50 units). The scale factor is 5.5.

To find the perimeter of TUV, we multiply the lengths of all sides of ABC by the scale factor. The perimeter of TUV is 5.5 times the perimeter of ABC. The perimeter of ABC is 40 + 50 + 24 = 114 units, so the perimeter of TUV is 5.5 times 114, which equals 627 units.