SOLUTION: Triangle ABC has area 240. 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.

Algebra ->  Triangles -> SOLUTION: Triangle ABC has area 240. 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.      Log On


   

Question 19257: Triangle ABC has area 240. 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.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F8%2B+1%2F5%2B1%2F6)) of ABC
= (61/120)*ABC = 122
Draw a diagram by yourself.
Kenny