The perimeter of the triangle is 11 cm, it is divided by the median into 2 triangles, the perimeter

The perimeter of the triangle is 11 cm, it is divided by the median into 2 triangles, the perimeter of which is 6 and 8 cm.Find the meliana of the triangle

Let the sides of this triangle be equal to a, b and c, and let the median d be drawn to side c and divide it in half. Knowing that the perimeters of the two triangles into which the median divides the given one are equal to 6 and cm, we compose the equations:

1) a + 0.5c + d = 6;

2) b + 0.5c + d = 8.

Solving the system by the method of algebraic addition, we get:

a + 0.5c + d + b + 0.5c + d = 6 + 8;

a + b + c + 2d = 14.

The perimeter of the given triangle is 11 cm, so a + b + c = 11. Thus:

11 + 2d = 14;

2d = 14 – 11 = 3;

d = 3/2 = 1.5 cm – the median of the triangle.