Two large holes are cut in a metal sheet shown below. If this material is heated, what can be said about distances AB and BC?

When matter is heated without any change in its state, it expands because with rise in temperature the amplitude of vibration increases and hence energy of atoms increases, hence the average distance between the atom increases. So the matter as a whole expands. Resulting in distance between any two points within the same object will be enlarged. Hence, both the distances AB and BC will increase.