this isn't scientifically mathematical, but it will get you in the ball park on what it should be.
I have quite a few of the military ALTERNATIVE COURSE "C" RECORD FIRE QUALIFICATION targets, it has scaled down silhouette targets. you place the target at 25 meters from the firing point, it has what silhouette targets would look like at 50meters to 300 meters.
the 200 meter man silhouette target on it is 4 inches high and 2.5 inches wide.
you said you already figured the height from 50 yards would be 12 inches high, so I would guesstimate the width would be something like a little more then half that, 6.5 or 7 inches or so. might even be a inch more wider, given there are a shit load of fat fucks now-a-days
like I said it's not scientific, but close enough for horseshoes and hand grenades