Quickest way without solving is to have ABC in a right triangle. BC and BA are the two sides = 50 with AC the hypotenuse = 60. Cut across from B to AC dividing the hypotenuse in half = 30. Call this point T. The new triangle ATB is in the 3:4:5 ratio or 30:40:50.
Bravo, ndidi204! 3:4:5, 5:12:13 are widely known Pifagorian numbers.