# The sides of the triangle are 2: 3: 5, and the perimeter of the triangle formed by its middle lines is 40 cm.

The sides of the triangle are 2: 3: 5, and the perimeter of the triangle formed by its middle lines is 40 cm. Find the middle lines of the triangle.

Since the middle lines of the triangle are equal to half the length of the sides to which they are parallel, then their length will have a ratio of 2: 3: 5.

Since the perimeter of the triangle formed by the middle lines (we denote it ABC) is 40 cm, and the sides are in the ratio 2: 3: 5, we express it as follows:

2x – AB side;

3x – aircraft side;

5x – speaker side;

2x + 3x + 5x = 40;

10x = 40;

x = 40/10 = 4;

AB = 2 4 = 8 cm;

BC = 3 4 = 12 cm;

AC = 5 4 = 20 cm.

Answer: the middle lines of this triangle are 8 cm, 12 cm, 20 cm.

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