Let A, B and C denote the vertices of a triangle with area 10. Let point D be on side AB,
point E be on side BC and point F be on side CA with AD = 2 and DB = 3. The area of
△ABE and the area of quadrilateral DBEF are the same. What is the value of this area?  Choose the correct choice from the following options.
A) 5.5
B) 6
C) 7
D) 8
E) 8.25
First, note that 4AFD and 4AFE have the same area. Therefore, ED is parallel to AF.   Since 4DEB and 4ACB are similar, BE=EC = 3=2. Thus, the area of 4AEB is 3=5ths of the   area of 4ABC.   correct answer 6
<result>B</result>
Let A, B and C denote the vertices of a triangle with area 10. Let point D be on side AB,
point E be on side BC and point F be on side CA with AD = 2 and DB = 3. The area of
△ABE and the area of quadrilateral DBEF are the same. What is the value of this area?