Joined: Aug 2010
Posts: 12,717
Likes: 2,104
From: Madison, WI
Bikes: 1961 Ideor, 1966 Perfekt 3 Speed AB Hub, 1994 Bridgestone MB-6, 2006 Airnimal Joey, 2009 Thorn Sherpa, 2013 Thorn Nomad MkII, 2015 VO Pass Hunter, 2017 Lynskey Backroad, 2017 Raleigh Gran Prix, 1980s Bianchi Mixte on a trainer. Others are now gone.
There is a wide range of arm lengths for V brakes. On one of my bikes I am near the short extreme of about 85mm, two of my bikes have the 110mm length. Longer gives you more leverage, and more tire clearance.
From the photo, yours look pretty long. And with fenders you need pretty long ones.
I assume you mean the adjustment screws that adjust spring tension to try to make both brakes go in and out together are broken. That is unusual for those to break. Can you remove the broken part of the adjustment screws to replace them? If they are a standard thread, like 4 mm, you may be able to get new stainless screws at a hardware store.
Tektro makes good V brakes that are quite affordable.