The sides of a triangle are 2: 3: 4. The large side of a similar triangle is 36 cm. Find the perimeter of two triangles.

1. Let’s denote the coefficient of similarity through x.

2. Let’s define the sides of this triangle:

2x cm, 3x cm and 4x cm.

3. Since the large side of such a triangle is 36 cm, compose and solve the equation:

4x = 36;

x = 36: 4;

x = 9.

4. The coefficient of similarity is 9.

5. What is the length of the middle side of the triangle?

3 * 9 = 27 (cm).

6. What is the smaller side of the triangle?

2 * 9 = 18 (cm).

7. What is the perimeter of the second triangle?

18 + 27 + 36 = 81 (cm).

Answer: the perimeter of such a triangle is 81 cm.