Answer: AC : BC = 22 : 33 = 2 : 3
Step-by-step explanation:
Since we have given that
AB = 3x-4
AC= 2x+12
BC = 7x-2
And AB: AC = 1 : 2
and To show : AC : BC = 2 : 3
So, it becomes ,
[tex]\dfrac{AB}{AC}=\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=\dfrac{20}{4}\\\\x=5[/tex]
So, AC: BC becomes:
[tex]\dfrac{AC}{BC}=\dfrac{3x-4}{7x-2}=\dfrac{2(5)+12}{7(5)-2}=\dfrac{22}{33}=\dfrac{2}{3}[/tex]
Hence, proved.
