2. A triangle with a perimeter of $55 \mathrm{~mm}$ is divided by a certain line segment into two triangles. Calculate the length of the line segment by which the original triangle is divided if the perimeters of the resulting triangles are $41 \mathrm{~mm}$ and $25 \mathrm{~mm}$.
2. Sketch of a triangle divided by a given line segment into two triangles:

1 POINT

![](https://cdn.mathpix.com/cropped/2024_05_30_cbc9d69bfef3283ff9a2g-1.jpg?height=705&width=696&top_left_y=1304&top_left_x=720)

The perimeter of the given triangle is less than the sum of the perimeters of the two resulting triangles by twice the length of the line segment that divided the initial triangle into two new triangles.

2 POINTS Therefore, it holds that:

$2 d=41+25-55$

1 POINT

$2 d=11$

$d=5.5 \text{ mm}$

1 POINT

The length of the given line segment is $5.5 \text{ mm}$.

1 POINT

TOTAL 6 POINTS