The perimeter of A is 20 cm.
The perimeter of B is also 20 cm.
The area of them is identical.
Are the rectangles congruent?
We have hundreds of course questions with personalized recommendations + Account 100% premium
The perimeter of A is 20 cm.
The perimeter of B is also 20 cm.
The area of them is identical.
Are the rectangles congruent?
To determine if the two rectangles are congruent, we start by understanding that two rectangles are congruent if they have identical lengths and widths. In this problem, both rectangles have a perimeter of 20 cm and identical areas, which suggests they could potentially be congruent.
Let's recall the formulas:
Perimeter of a rectangle:
Area of a rectangle:
Given that each rectangle has a perimeter , we can write:
for Rectangle A,
for Rectangle B,
which simplifies to:
,
.
The identical area condition gives us:
.
Given that both the sums of and (using perimeter) and their products (using area) are equal, this enforces that and .
This implies that the rectangles are congruent (i.e., have identical lengths and widths).
Therefore, the solution to the problem is Yes.
Yes
Are the rectangles congruent?
They can't! When rectangles have both identical perimeter and area, the mathematical constraints force them to have exactly the same dimensions, making them congruent.
Then they could be different! A 6×4 rectangle and a 7×3 rectangle both have perimeter 20, but different areas (24 vs 21). You need both conditions to guarantee congruence.
Show that their corresponding sides are equal. Use the constraints: and to prove and .
Yes for just perimeter! But when you add the identical area constraint, it becomes a unique solution. The two conditions together eliminate all other possibilities.
Congruent rectangles are exactly the same size and shape - they have identical length and width. You could place one on top of the other and they'd match perfectly.
Because similarity only requires same proportions, while congruence requires identical actual dimensions. The specific perimeter and area values determine exact size, not just shape.
Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime