Final answer:
Using the properties of perpendicular bisectors and triangle inequalities, we can determine the length of BC in terms of m.
Step-by-step explanation:
Given that AD is the perpendicular bisector of BC, we can use the properties of perpendicular bisectors to find the length of BC.
Since AD is the perpendicular bisector of BC, it divides BC into two equal halves, so BD = DC.
Also, using the properties of a triangle, we have AB + BC > AC and AC + BC > AB. Plugging in the given values, we get 12 + BC > m/6 and m/6 + BC > 12.
From the given information, we can determine that DC = 0.25m/2 = 0.125m. Therefore, BD = 0.125m. To find BC, we solve the inequality 0.125m + BC > 12:
0.125m + BC > 12
BC > 12 - 0.125m
So, BC is greater than 12 - 0.125m.