Let's analyze and solve the problem step by step.

Step 1: Define Variables

Let:

• The length of $AB = l$ (the longer side of the rectangle).
• The length of $AD = w$ (the shorter side of the rectangle).

Then, the area of the rectangle $ABCD$ is given by: $\text{Area of } ABCD = l \cdot w$

Step 2: Given Information about the Parallelogram's Area

We know the area of parallelogram $AECF$ is three-fifths the area of rectangle $ABCD$: $\text{Area of } AECF = \frac{3}{5} \cdot (l \cdot w)$

Step 3: Relationship between $EB$ and $CB$

It is given that $CB$ is 25% less than $EB$. So, if $EB = x$, then: $CB = x - 0.25x = 0.75x$ Since $CB = w$ (the height of the rectangle), we can say: $w = 0.75x$ or equivalently, $x = \frac{w}{0.75} = \frac{4}{3}w$

Step 4: Perimeters of Rectangle and Parallelogram

The perimeter of the rectangle $ABCD$ is: $\text{Perimeter of } ABCD = 2(l + w)$

To find the perimeter of the parallelogram $AECF$, note that opposite sides of a parallelogram are equal. The two pairs of opposite sides are $AE$ and $CF$, and $AF$ and $EC$. Since $AECF$ is inscribed in $ABCD$, the lengths of these sides align with parts of $ABCD$:

• $AE = AB = l$ (since $E$ lies on $AB$).
• $AF = AD = w$ (since $F$ lies on $CD$).

Thus, the perimeter of parallelogram $AECF$ is: $\text{Perimeter of } AECF = 2(l + w)$

Step 5: Percentage Difference in Perimeters

Since both the rectangle and the parallelogram share the same perimeter, the percentage by which the perimeter of $ABCD$ is greater than the perimeter of $AECF$ is: $\frac{(2(l + w) - 2(l + w))}{2(l + w)} \times 100 = 0\%$

Conclusion

The perimeter of the rectangle $ABCD$ is 0% greater than the perimeter of the parallelogram $AECF$.

Would you like a deeper explanation of any step?

Here are five related questions:

1. How does changing the proportion of $AE$ to $AB$ affect the area of the parallelogram?
2. How would the solution change if the area of the parallelogram were different from three-fifths of the rectangle's area?
3. What is the perimeter relationship if the parallelogram were tilted within the rectangle?
4. How would the answer change if $CB$ were a different percentage less than $EB$?
5. Can this approach be used for other quadrilaterals within rectangles?