Similar Triangles and Rectangle EFGD: Calculate Perimeter Using 3, 6, and 8 Units

To solve for the perimeter of rectangle $EFGD$, we follow these steps:

Step 1: Use the similarity of the triangles $\triangle BCD \sim \triangle FED$. This implies the sides are proportional:

Substitute the known lengths $CD = 8$ and $ED = 3$:

Solving for $EF$, cross-multiply:

Step 2: The length and width of rectangle $EFGD$ are $2.25$ (as calculated from $EF$) and $3$ (equal to $ED$).

Step 3: Calculate the perimeter $P$ of $EFGD$:

The perimeter of rectangle $EFGD$ is $10.5$.