What length of rope do i need to climb the matterhorn?

What you NEED is a guidebook! You can't be thinking of doing a technical route up the Matterhorn without a guidebook or at the Very least some printed notes and sketches, or you will probably be getting lost and endangering yourself, as well as being really unprepared for what lies ahead. Having said that, a lot of Alpine routes have abseils of 25-30m in them, so you would either need a 60m-70m single rope (i.e. 10mm diameter roughly), or a pair of half ropes (8mm roughly). I don't know whether this is the case with the Matterhorn, but in general it's a good idea to have this amount of rope. If you're doing a non-technical route up it (I don't know that if there is one) then again get a guidebook and see what it says about rope and gear. As for 'type of rope', hopefully I've covered that above, but you'll definitely be wanting a dynamic climbing rope if you're doing anything that needs rope, rather than a static 'abseil' or 'caving' rope, which aren't designed to take falls.

since you are only 15, about 10 feet of your Mom's clothesline should do it.