[ Perimeter of a Triangle ]

On side $A C$ of triangle $A B C$, point $E$ is marked. It is known that the perimeter of triangle $A B C$ is 25 cm, the perimeter of triangle $A B E$ is 15 cm, and the perimeter of triangle $B C E$ is 17 cm. Find the length of segment $B E$.
$15+17=P_{A B E}+P_{B C E}=P_{A B C}+2 B E=25+2 B E$. Therefore, $B E=(32-25): 2=3.5$.

![](https://cdn.mathpix.com/cropped/2024_05_06_970e9bfb17ad7b5a0e46g-18.jpg?height=409&width=761&top_left_y=1282&top_left_x=657)

## Answer

3.5 cm.