Given
ramp = rise + 50
run = rise + 49
ramp² = rise² + run² (Pythagorean theorem)
Find
rise, run, ramp
Solution
Substitute the given values into the Pythagorean theorem equation and solve.
... (rise +50)² = rise² + (rise +49)²
... rise² +100rise +2500 = rise² +rise² +98rise +2401
... rise² -2rise -99 = 0 . . . . . subtract the left side
... rise² -2rise +1 = 100 . . . . .add 100
... (rise -1)² = 10² . . . . . . . . . rewrite as squares
... rise -1 = 10 . . . . . . . . . . . . take the positive square root
... rise = 11
... run = 11 +49 = 60
... ramp = 11 +50 = 61