Answer:
AC : BC = 22 : 33 = 2 : 3
Step-by-step explanation:
It is convenient to find the value of x first.
AB/AC = 1/2 = (3x -4)/(2x +12)
Cross-multiplying gives ...
2x +12 = 2(3x -4)
2x +12 = 6x -8
20 = 4x . . . . . . . add 8-2x to both sides
5 = x . . . . . . . . . . divide by 4
___
So the side lengths are ...
- AB = 3x -4 = 3·5 -4 = 11
- AC = 2x +12 = 2·5 +12 = 22
- BC = 7x -2 = 7·5 -2 = 33
Then the ratio of interest is ...
AC : BC = 22 : 33
AC : BC = 2 : 3 . . . . . . (divide by 11 to simplify)
_____
Comment on the triangle
We note that AB+AC=BC, so this "triangle" is actually a line segment 33 cm long.
