Twin Paper Folding
Twins Tweedledee and Tweedledum are given a rectangular piece of paper of the same size.
They each fold their paper in half, parallel to one of the sides.
Tweedledee calculates that the perimeter of his rectangle is 40.
Tweedledum calculates that the perimeter of his rectangle is 50.
What is the perimeter of the original piece of paper?
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1 solution
Without loss of generality, let x be 1 side and y be the other side, where x > y
The perimeter of any shape is given as P = 2 x + 2 y . Since Tweedledee and Tweedledum are folding their papers in half, the perimeter of this new shape is given as P = x + 2 y and P = 2 x + y .
Again, without loss of generality, x + 2 y = 4 0 and 2 x + y = 5 0 . Adding these equations gives 3 x + 3 y = 9 0 .
Since we are trying to find the perimeter of the original shape which is 2 x + 2 y , we get x + y = 3 0 and then P = 2 x + 2 y = 6 0 .
Hence the original perimeter is 6 0