There are two possible cases as follows
Case 1: Let side #9# of triangle B be the side corresponding to the small side #3# of triangle A then the ratio of areas #\Delta_A# & #\Delta_B# of similar triangles A & B respectively will be equal to the square of ratio of corresponding sides #3# & #9# of both similar triangles hence we have
#\frac{\Delta_A}{\Delta_B}=(3/9)^2#
#\frac{5}{\Delta_B}=1/9\quad (\because \Delta_A=5)#
#\Delta_B=45#
Case 2: Let side #9# of triangle B be the side corresponding to the greater side #9# of triangle A then the ratio of areas #\Delta_A# & #\Delta_B# of similar triangles A & B respectively will be equal to the square of ratio of corresponding sides #9# & #9# of both similar triangles hence we have
#\frac{\Delta_A}{\Delta_B}=(9/9)^2#
#\frac{5}{\Delta_B}=1\quad (\because \Delta_A=5)#
#\Delta_B=5#
Hence, maximum possible area of triangle B is #45# & minimum area is #5#
