If two triangles have equal area and stand on the same base, then the altitudes of the triangles are equal.
True
Triangles on the same base (or equal bases) and having equal areas have equal altitudes.
This can be easily proved. Take two triangles: triangle-1 and triangle-2 having same base 'b' and altitudes 'c' and 'd' respectively.
Area of Triangle-1 = 12×b×c
Area of Triangle-2 = 12×b×d
Since the triangles have the same area, c = d