The sides of the triangle are in the ratio 3: 4: 6. By connecting the midpoints of all sides

The sides of the triangle are in the ratio 3: 4: 6. By connecting the midpoints of all sides, we got a triangle with a perimeter of 5.2 cm. Determine the sides of this triangle.

Let’s denote the first side of this triangle 3x, then the second side of this triangle is 4x, and the third side of this triangle is 6x. The sum of all the sides of such a triangle is 5.2 centimeters. Let’s make the equation:

3x + 4x + 6x = 5.2.

Let’s solve the equation and find the unknown x:

13x = 5.2.

x = 5.2: 13.

x = 0.4.

Find the first side of the triangle:

3 * 0.4 = 1.2 centimeters.

Find the second side of the triangle:

4 * 0.4 = 1.6 centimeters.

Let’s find the third side:

6 * 0.4 = 2.4 cm.

Answer: 1.2 cm, 1.6 cm, 2.4 cm.