Parallel covering of isosceles triangles with squares

Suppose that T^h is an isosceles triangle with base length 1 and with height h. Let S be a square with a side parallel to the base of T^h and let {S_n} be a sequence of the homothetic copies of S. We first determine the bound of sums of areas of squares from the sequence {S_n} that permits a parallel covering of T^h. Then we show that the results about covering isosceles triangles are also true for acute or right triangles.