Given a rectangular cake with a rectangular piece removed(of any size and orientation) how can you cut the rectangle in two equal parts with one straight line cut of a knife.
Note:- The cut is of any size and any orientation, it means the removed piece can be one of the layer of the cake.
See Rectangular cake puzzle Solution
Rectangular cake puzzle solution
You can cut the cake by the line joining the center of the original cake and the center of the removed piece, this will divide the rectangle in exactly two pieces.
We can use the fact that “any line passing through the center of a rectangle divides the rectangle in two equal pieces.”
Thus in above image:- x1 should be equal to x2 and y1 should be equal to y2.
Area of the top part = x1 – y1
Area of the bottom part = x2 – y2
But as x1 = x1 and y1 = y2=> Area of the top part should be equal to Area of the bottom part