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.
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