Rectangle Congruence: Comparing Two Rectangles with Areas A=24 and A=20

To determine whether the rectangles are congruent, we need to understand what congruence means for geometric figures.

Definition of Congruent Rectangles:
Two rectangles are congruent if and only if they have exactly the same dimensions. This means they must have the same length and the same width. Congruent figures can be placed on top of each other through rigid motions (translation, rotation, reflection) and match perfectly.

Key Observation:
An important property of congruent figures is that they must have equal areas. While equal areas don't guarantee congruence for rectangles, different areas guarantee that the rectangles are NOT congruent.

Analysis of the Given Rectangles:
From the diagram, we can see:

• Rectangle 1 has area $A = 24$
• Rectangle 2 has area $A = 20$

Conclusion:
Since the two rectangles have different areas ($24 \neq 20$), they cannot possibly have the same dimensions. Therefore, the rectangles are not congruent.

The answer is: No