Half the area of an L


Two arbitrary rectangles are placed to form an “L”.  That is, the lower left-hand corner of the two rectangles share the same point. (What I’m trying to say is that there’s an “L” whose “I” and “_” parts have arbitrary widths and heights.) Using only a (pen and a) straightedge (that is, no measuring device and no compass), figure out a way to, with a single straight cut, divide the “L” into two pieces of equal area.

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    draw a vertical line from the right bottom of the L-shape and a horizontal line from the left top of the L-shape do that this two lines meet each other.
    This gives us 3 squares: the right lower part of the L-shape (lets call it rectangle C), The vertical rectangle of the L-shape (lets call it rectangle B), and the new rectangle between them (let call it rectangle A).
    Since Any line passing through the center of a rectangle divides it in half we find the center of rectangle A by drawing the intersecting diagonals.
    We do the same for the square made up from the 3 rectangles (A,,B,C), and so the line passing threw 2 two points divides the L-shape into 2 equal parts.

    Moshe Expert Answered on 23rd March 2023.
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