Calculate Rectangle Perimeter Using Congruent Triangles: 6 and 8 Unit Measures

To find the perimeter of rectangle EDGF, we will follow these steps:

• Step 1: Recognize congruence $\Delta BCE \equiv \Delta FED$.
• Step 2: Use congruent triangles to find side lengths of ED and DF.
• Step 3: Calculate the perimeter using the formula for rectangles.

Now, let's proceed with the solution:

Step 1: Given $\Delta BCE$ and $\Delta FED$ are congruent triangles, their corresponding sides are equal. Thus, since $BC = 6$, it follows that $ED = BC = 6$.

Step 2: From the configuration of the rectangle, note that $FE$ (same as AE) is given to be 8, hence $GF = 8$ because EDGF is a rectangle.

Step 3: The perimeter of rectangle EDGF can be calculated using:

Therefore, the solution to the problem is that the perimeter of rectangle EDGF is 28.