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Are the geometric and circumferential dimensions the same at the same time?
Not necessarily/possibly

For example:

Rectangular: 5 cm long and 3 cm wide.

Circumference = (length+width) ×2= (7+4)×2=22cm

Rectangular with equal circumference: 6 cm long and 5 cm wide.

Circumference =(6+5)×2 = 22 cm

The area of the first rectangle = length× width =5×3= 15cm?

The area of the second rectangle =6×5=30cm?

So they have the same circumference but different areas.