Confused on a question (1 Viewer)

[study123456]

Hi, got stuck on a question,
The rest length of a train is 200 m and the rest length of a railway platform is 160 m. The
train rushes past the platform so fast that, when observed in the platform’s frame of
reference, the train and the platform are the same length.
How fast is the train moving?

So what i did
lv= l0sq 1- v^2/c^2
(lv/10) = 1- v^2/c^2
(!60/200)^2- 1= v^2/c^2
-0.36= -v^2/c^2
0.36 =v^2/c^2
0.36/(3x10^8)^2 = v^2
4x 10^-8 = v^2
sq root 4x 10^-18

= 2x 10^-9

Now, i know this wrong, but our teacher showed us this way, and now i am confused that how to get the real answer

 

[YeetusMaximus]

lv=lo rt(1-v2/c2)
lv/lo = rt (1-v2/c2)
(lv/lo)^2=1-v2/c2
v2/c2=1-(lv/lo)^2 (rearrange)
v2=c2 x (1-(lv/lo)^2)
v=c x rt(1/-(lv/lo)^2)
v=3x10^8 x rt(1-160^2/200^2)
v=1.8 x 10^8

 

[YeetusMaximus]

Don't forget units