[ The ratio in which the bisector divides the side. ] [ Thales' Theorem and the theorem of proportional segments ]

On each side of the rhombus, there is one vertex of a square, the sides of which are parallel to the diagonals of the rhombus.

Find the side of the square if the diagonals of the rhombus are 8 and 12.
By cutting the rhombus along its diagonals, we reduce the problem to the following.

Find the side of the square $C K L M$ inscribed in the right triangle $A B C$ ($K, L, M$ lie on the sides $A C, A B$, and $B C$ respectively) with legs $A C=6, B C=4$.

For further details, see problem $\underline{54659}$.

## Answer

4.8 .