4.3. Through the vertex $A$ of the parallelogram $A B C D$, a line is drawn intersecting the diagonal $B D$, the side $C D$, and the line $B C$ at points $E, F$, and $G$ respectively. Find $E D$, if $F G$ : $F E=7, B E=8$. Round your answer to the nearest hundredth if necessary.
Answer: 2.83 (exact value: $2 \sqrt{2}$ ).