Question 19257
 Points X,Y,Z lie on sides AB,BC, and CA, respectively. Given that segment AX/BX=3, BY/CY=4, CZ/AZ=5, find the area of triangle XYZ.

 Consider the area of triangle AXZ, BXY & CYZ,

 Area of AXZ : ABC = (AX/AB)/(AZ/CA) = (3/4)*(1/6) = 1:8 ,
 Area of BXY : ABC = (BX/AB)/(BY/BC) = (1/4)* (4/5) = 1:5 ,
 Area of CYZ : ABC = (CY/BC)/(CZ/CA) = (1/5)*(5/6) = 1:6 ,

 Hence,XYZ = ABC -(AXZ + BXY + CYZ) = (1-({{{1/8+ 1/5+1/6}}})) of ABC
 = (61/120)*ABC = 122

 Draw a diagram by yourself.

 Kenny