The sides of the triangle are 4: 7: 9, and the longest side is 45 cm. Find the perimeter of the triangle.

1. From the ratio of the lengths of the sides, it is clear that the largest side is the one that has 9 parts. Then we divide 45 cm into 9 parts, we get the length of one part:

45/9 = 5 cm.

2. Find the other two sides of the triangle by multiplying the number of their parts by the length of one part:

1 side = 4 * 5 = 20 cm.

2 side = 5 * 7 = 35 cm.

3. Find the perimeter of the triangle by adding the lengths of its three sides:

45 + 20 + 35 = 45 + 55 = 100 cm.

Answer: the perimeter of the triangle is 100 cm.