Problem E : 6700 , page 413 , GMB 11/1979

From GAZETA MATEMATICA series B

ANSWER CiP  

diagonals  =  a and  a\sqrt{2}

4-th side  = 0,5a(\sqrt{6}-\sqrt{2})

SOLUTION  CiP

The figure for the problem is as follows:

The hypothesis and conclusion

For calculating the diagonals