6)

The large triangle is isosceles. The altitude to the base divides it into two right-angled triangles. The base is divided into three equal segments. The altitude is $$12$$ cm. $$y$$ is the altitude of one of the smaller triangles. Using Pythagorean theorem on the left small triangle, $$y^2 + (x)^2 = (2x)^2$$, where $$x$$ is the length of the smallest segment. $$y^2 = 3x^2$$. Using Pythagorean theorem on the large triangle, $$(3x)^2 + 12^2 = (2 imes ext{hypotenuse})^2$$. This problem is unsolvable with the given information.