My MTB has 29" x 2.25" tires on it now. I'm looking at these 700mm x 35mm tires to replace them. Will they fit a 29" rim?
Three factors to check:
Factor 1. Diameter. If your wheel is a standard 29", then it equals 700c or 622mm. They are different convension name of the same diameter for different types of bicycle markets.
29" = 700c = 622
Factor 2. Clearance
Since, 35mm is much narrorer than 2.25" (~57mm), the clearance will not be any problem at all. Your current bicycle frame will have much clearances to install 35mm tyres.
Factor 3. The specificiation of the wheelset
The final factor to check is to go through the specification of the wheelset.
The official specification will tell if the tyre width is compatible with the wheel.
For an example: MAVIC Crossmax Pro <-- A MTB XC wheelset
In the specification of it, you will see
#1 The RIM size is ETRTO size 29": 622x22TSS
#2 Recommended tyre sizes: 46mm to 64mm (1.8" to 2.5")
Since 35mm is narrorer than the official recommendation, in the case of MAVIC Crossmax Pro, it will be not recommended to install a 700x35C tyre.
PS. Please don't argue the marketing or not marketing with me. It is a free world. Anyone can try any not recommended combination as his/her free willings but I just can't give the answer of the kind.