Question

If two rectangles have the same perimeter, do they have to be congruent? Explain how you know.

Answer 1

No

Explanation:

Take square 4 X 4. Perimeter =16

Take rectangle h2 X w6. Perimeter =16

Clearly the same perimeter and not congruent

but this is just what I think

Answer 2

Explanation:

Suppose one of them is a perimeter of 24

P = 1 + 1 + 11 + 11

P = 24

The second one has these dimensions

P = 4 + 4 + 8 + 8

P = 24

Do they look like they could be congruent to you? The first one looks long and narrow.

The second one looks like it's heading to be a square. (It's not of course, but it is closer than the long narrow one).