Find the ratio of the area of \(\triangle BCX\) to the area of \(\triangle ACX\) in the diagram if CX bisects \(\angle ACB\). Express your answer as a common fraction. 
+128475 Let AX = M
Let BX = 24 - M
Since ACB is bisected, we have this relationship
M / 30 = (24 - M) / 27 cross-multiply
27M = 30( 24 - M) simplify
27M = 720 - 30M add 30M to both side
57M = 720
M = 720 / 57 = 240 / 19 = AX
Then 24 - M = 24 - 240/19 = 216/19 = BX
Since each triangle is under the same height, the ratio of their areas is just the ratio of their bases
So
area BCX / Area ACX = ( 216 /19) / (240 / 19) = 216 /240 = 9 / 10
