Final answer:
To find the perimeter of the original sheet of paper, we set up a system of equations based on the two different cuts. Solving the system gives us a perimeter of 57 cm for the original sheet of paper.
Step-by-step explanation:
To find the perimeter of the original sheet of paper, we need to consider the two different ways it can be cut and determine the dimensions of each resulting rectangular piece. Let's denote the original length of the paper as l and the original width as w.
When the paper is cut such that each resulting piece has a perimeter of 50 cm, we can set up the equation 2(l/2 + w) = 50. Simplifying this equation gives l + w = 25.
When the paper is cut the other way and each resulting piece has a perimeter of 64 cm, the equation becomes 2(w/2 + l) = 64, which simplifies to w + l = 32.
We now have a system of equations: l + w = 25 and w + l = 32. Adding these equations together eliminates l and gives us 2w = 57. Solving for w, we find that w = 28.5 cm.
Substituting this value into either of the original equations gives us the value of l, which is also 28.5 cm.
To find the perimeter of the original sheet of paper, we add the length and width together: 28.5 cm + 28.5 cm = 57 cm.
Learn more about Perimeter of a rectangle