Correct solutions were received from Surendra Dhir, Agustin Murillo, Juan Marivela, Paul Botham, Al Zimmermann, Bill Webb, Aaron Kahn, Steve Prowse, Nancy Schwarzkopf, Lou Cairoli, Juan Carrara, Burkart Venzke, Alejandro Vellano, Ron Welch, Aaron Kahn, Jens Vob, .

Figure 1 on the far left shows one possible configuration. Draw two lines parallel to the diagonal AC at the points B and D as shown.  Now grab the point D and drag it up or down along the line while leaving the point O fixed until the diagonal BD becomes perpendicular to AC as in figure 2.  As you do this, the area of the triangles do not change -- note how both the base and the height of each of them remain the same!  Place a coordinate system on the figure with O at the origin and with axes along the diagonals in such a way that the point B is at (-1,0).  The conditions on the area of the triangles forces A = (0,-2), C = (0,4) and D = (6/4,0).  Triangle AOD is uniquely determined to have area 3/2.  

You are visitor number  2800 to this page.