Observing Triangle Inequality Closely

Lew W.S.
Look closely at how the lengths of the sloping sides of the triangle below add up as the apex of the triangle is almost touching the base of the triangle! In activity at https://www.geogebra.org/m/JT5UmZ8w , in which lengths were rounded to integers, it appears that a triangle can be formed even if the length of the two sloping sides add up to 12 when the base is also 12 units. In the triangle below, the sum of the sloping sides will always be greater than 12, unless the triangle disappears when the apex (C) touches the base AB