Are the rectangles below congruent?
Are the rectangles below congruent?
Are the rectangles below congruent?
Are the rectangles congruent?
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?
Are the rectangles congruent?
Are the rectangles below congruent?
Since there are two pairs of sides that are equal, they also have the same area:
Therefore, the rectangles are congruent.
Yes
Are the rectangles below congruent?
We can see that the length is identical in both rectangles: 3=3.
However their widths are not equal, as one is 2 while the other is 4.
Therefore, the rectangles are not congruent.
No
Are the rectangles congruent?
Note that DC divides AE into two unequal parts.
AC=5 while CE=4
The area of rectangle ABDC is equal to:
The area of rectangle CDGE is equal to:
Therefore, the rectangles do not overlap.
No
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?
No