JJJ.13 Area ratio divided in triangle

In a figure below, AE : EC = 2 : 3, AF : FB = 3 : 1 and the area ratio of the triangle ABC and the triangle DEF is 40 : 9.

Answer the following questions.

(1) Find the area ratio of the triangle BEF and the triangle DEF by the ratio of the least integer.

(2) Find the area ratio of the triangle DEF and the triangle CEF by the ratio of the least integer.

(3) Find BD : DC by the ratio of the least integer.

Answer

(1) 4 : 9
(2) 1 : 2
(3) 5 : 9

Reference