C172 flight instructor reported brake failure on landing resulted in a runway excursion off the end of the runway.

Narrative

On Day 0 at approximately XA00 I was flying Aircraft X and had a runway excursion. Probable cause: Contributing factors to this incident are the left brake failure upon landing; a higher than normal idle setting; and a slightly higher than normal approach airspeed. Recurrence prevention: Maintenance performed to brakes and address the high idle; although idle is within spec. Pilot proper adherence to procedures outlined in the POH and a willingness to squawk aircraft even for very minor issues. Details about the incident: The airplane had recently come out of its 100 hour inspection and this was the third flight after the inspection was performed. Myself and other instructors had noticed prior to the inspection the brakes seemed a little weak but it was nothing that seemed worthy of being reported. After the 100 hr inspection there seemed to be no issues. On the incident flight a preflight was performed by both the student and myself together. The brakes were inspected and no defects were visible.The flight was a training flight with a student in the left seat and myself in the right seat. A brake check was performed on the left and right side prior to departing the ramp and no issues were detected. The idle was checked as well at this time and verified to be approximately 1000-1100 RPM. This flight focused on maneuvers and the maneuvers were flown in the practice area north of the airport. After about one hour of flying we came back.I took controls for the remainder of the flight; called inbound to ZZZ Tower and was requested to perform a standard straight in approach to Runway XX with traffic in front and behind me. The spacing of traffic in front was close and I was requested by Tower to perform an S turn to increase spacing. The S turn was completed approximately 0.5-1.0 miles prior to the threshold. My airspeed was slightly high; approximately 75 kts on the approach due to the S turn. The normal approach speed for this airplane that day would have been 65 kts. I crossed the threshold at or slightly below the visual glide path indicator and touched down between Taxiway 1 and 2; around the 4th or 5th centerline stripe after the numbers. This is slightly beyond my intended touchdown point but I felt it was within reasonable limitations. The high idle causes some additional float. After touchdown both brakes were applied evenly but the airplane veered to the right suddenly. The left brake pedal went all the way down to the floor and had no pressure. I asked my student in the left seat to help apply brakes but had the same result. From that point in order not to go off the right side of the runway at high speed; the decision to discontinue brake application was made in order to dissipate speed going straight forward. The airplane was kept in the center of the runway until it went off the end into the dirt about 10 feet off the edge. This excursion resulted in no further damage to the airplane; airport property; nor was anyone injured. The Tower and Airport Operations acted very quickly and met me at the airplane to assist me. The airplane was pushed onto the taxiway and moved to the ramp.