You are given two line segments, one is four times as long as the the other. The longer line segment is equal to the perimeter of an isosceles triangle. The shorter is equal to an altitude of the triangle.

Find a straightedge and compass construction of the triangle if the given altitude is perpendicular to the base.

Show that a straightedge and compass construction of the triangle is impossible if the given altitude is perpendicular to one of the congruent legs.