For what value of a is there a right triangle with sides a+1, 6a, and 6a+1?
Use Pythagoras: (a+1)2 + (6a)2 = (6a+1)2
a2 + 2a + 1 + (6a)2 = (6a)2 + 12a + 1
a2 -10a =0
a = 0 or a = 10.
Since we can’t have a triangle with length 0 (6a), we must have a = 10.