Question

there are two identical figures with all sides of equal lenght. the combined perimeter of the figures is 80 centimeters. what shape are the figures? what is the lenght of one side?

Answer 1

So we have two shapes that are exactly the same.  All their sides are of equal length.  The combined perimeter is 80 cm.  Since they're identical, we can safely say that the perimeter of EACH figure is 40 cm.  Let's work from that.  Remember, the perimeter is the length of all the sides of a figure added together.

What's the first shape that comes into your mind when you think of "equal length sides"?  Probably a square: a four-sided shape where all the sides are the same length.  If this were a square, and its perimeter is 40 cm, then the length of each side is 1/4 of 40 cm, right?  (Because there are 4 sides, and the perimeter is the length of all the sides combined.)  This would make the length of each side 10 cm.

Let's check.  If each side is 10 cm, and all 4 sides of the square are equal (which they are), the perimeter of each square is 40 cm.  The combined perimeter is 40+40=80 cm.  This works!

Answer: The figures are squares; each side is 10 centimeters long.