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It is always easier to hang something that is lighter, especially if you don't have any help. So separating the mirrors from the hinge could make the task less superhuman! Before you separate them, read on... there are reasons why you might not want to!
Since you are dealing with a ridiculously heavy item... glass on particleboard... my first thought is to use the heaviest super duper way I know of to hang anything on a wall. You will attach a wood hanging strip on the back of the mirrors and a mating strip on the wall. These strips will interlock, holding the mirror to the wall securely and making hanging and removal (if necessary) much easier. A second advantage to this method is that leveling the mirror is a piece of cake, since you do all the leveling on the hanging strips. Once the mirror is in place, it will be level unless Mother Nature sucks your home into the earth!
Screw and glue a strip of 1x2" pine, approximately two inches shorter than the distance across the back of each mirror or pairs of mirrors. Predrill the holes in the particle board and the strips for maximum strength. Be sure to use flat head wood screws or drywall screws and be careful with the length. If you drive the screws too deeply or use screws that are too long you will crack the mirror and have to make a trip to the dump! This strip should be located a few inches down from the top, a few inches less in length than the width of the mirror, centered horizontally and perfectly parallel to the top edge. Then, install a similarly sized piece of thin 1/8" plywood over the 1x2, screwed and glued, but have it extend slightly below the 1x2 so that you have a "lip". To make your work a little easier, you can preassemble the hanging strips and then attach them to the mirrors (and the wall, below).
Install an identical 1x2 and plywood strip level on the wall in the position you want it. Note that the overlap forming the two "lips" should be identical on both strips. But for the wall strip, remember to locate the "lip" on the top. Here is the one time where keeping the two mirrors double-width is an advantage. You have a total width of about 32", which should give you at least two of the wall studs to screw into. Using a single width of mirror will only allow you to have one stud behind each mirror, forcing you to use toggle anchors. Toggles will hold the mirror... use a 3/16" toggle for extra strength... but screwing into a firm stud is even better!
Hanging the mirror is easy...the two "lips" will interlock like two kids with braces (smack!!) holding the heavy mirror firmly in place. You might also want to install a 1x2 spacer across the bottom of each mirror to square it up on the wall and also so that the mirror won't pivot or swing on the top support. A really good idea!
The only problem with this method is that it positions the mirror quite a bit from the wall. However, you can use other materials, such as 1/2" plywood strip instead of the 1" pine to slightly reduce the thickness. You could also use a piece of flat iron instead of the plywood "lip" to further reduce the thickness. Of course with the metal you would be better attaching the wood to the mirror first, then the metal strip. Preconstructing would force you to drill through the metal adding to the difficulty of the job.
If you have more woodworking power tools available, a neat option would be to use an electric router or table saw to cut the "lip" right into the pine 1x2, saving the extra assembly and material thickness.
I will also offer a non-carpentry alternative which has its pluses and minuses. Visit your local hardware store and look for a type of hanging ring that would attach to the back of the mirror with screws. This is a metal ring that pivots on a steel strip with multiple screw holes (use a minimum three-holer for this installation), allowing its use for a variety of hanging projects. Predrill the holes for the screws, and use the largest size sheetmetal screw that will easily fit through the holes in the hanging rings. Remember not to get screws that are too long!
You will have to install nails or screws into the wall to hang the rings on. Depending on your walls, you might be able to screw right into the studs (if they are in the right places) or you will have to use molly anchors. Use the 3/16" size and be sure to get a hanging ring that is large enough to go over the top of the molly's screw head.
It will be more difficult to position the hardware properly and to level the mirror using this method, but it can be done with scrupulous measuring and patience. The key is the get the hanging rings in perfect position on the mirrors first, and then transferring this measurement to the wall. A trick... do not install all the screws through the hanging ring strips on your first try. Instead, install only the bottommost screws. Do a test hang. If the mirror is level, take it down and install the rest of the screws. If not, you can reposition one of the hanging rings slightly, using the remaining screw holes. Screwing into particle board weakens it, so you cannot locate two screws less than about 1/4" apart and expect the strongest grip.
I could come up with more variations on this theme, but time and space does not permit. Hope this is helpful.
It depends on who installed it and how. Remember... this is not the Psychic Network! My first impression... sensing your doubts... is I wouldn't take a chance with a mirror that large.
Plaster is a difficult material to hang stuff on. I have found plaster walls to vary dramatically in their ability to hold picture hangers. However, using #8 or #10 (at least a couple of inches long) hexhead screws through the plaster and into the lathe will give you great strength in most plaster walls. Of course, the strongest method is to install the screws into the wall studs, though the studs are seldom in the right place. A subcategory of Murphy's Law, I think.
Start the screw hole with a drill bit smaller than the screw. Don't drill through the lathe, just start the hole so the screw grabs in the plaster. You can use a masonry bit, but I have found that regular bits will work in most plaster walls but will become dull. A regular bit will drill a cleaner hole than a masonry bit.
You must test the screws for strength. Use a hammer or pair of pliers and exert steady downward force on the screw head, at least equal to the weight of the mirror. If the screw seems firmly attached, you are probably all right. Subjective judgement is all you have here!
I always put a small metal washer on the screw before attaching it to the wall. Place the mirror's hanging wire between the washer and the wall. This will prevent the wire from "jumping" off the screw head. With a heavy object, it is sometimes difficult to get the wire between the washer and the wall... especially when working solo! When this happens... and if getting a helper is impossible... stabilize the washer using a small amount of hot melt glue, Goop, or adhesive caulk between the washer and the screw head, and let it dry. In a pinch, you could even use some of that tacky gum… I think it's called Fun Tack… that kids often use to hold papers and other light objects to their walls.
If the plaster/lathe does not hold the screws well, you may have to install a strip of 1x3 1" pine or plywood between studs that will be hidden behind the mirror. Attach your hanging screws to the wood strip to locate the mirror.