Hi there,
I have to teach in some minutes, so I will give the "key", if needed anything else to understand, please write and when I finish I come back.
Regards,
Fabio.
From the similarity of triangles (angle S common, the other is the given in the question stem...) we get:
x over (4x) = 4x - (x+20) over 2x
For me x is the length of PT (and ST) ... please have a look and I hope you understand.
The answer is x = 8 then 12x equals 96!!
Hint in general for similarity: look angles opposing sides, then you will know which side must be proportional to which side... I hope you got it. I must teach now!