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

January 17, 2021 | education

| **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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