# Problem 309: Integer Ladders

![graphic](img309.gif)

In the classic "Crossing Ladders" problem, we are given the lengths x
and y of two ladders resting on the opposite walls of a narrow, level
street. We are also given the height h above the street where the two
ladders cross and we are asked to find the width of the street (w).
Here, we are only concerned with instances where all four variables are
positive integers. For example, if x = 70, y = 119 and h = 30, we can
calculate that w = 56. In fact, for integer values x, y, h and 0 < x
< y < 200, there are only five triplets (x,y,h) producing integer
solutions for w: (70, 119, 30), (74, 182, 21), (87, 105, 35), (100, 116,
35) and (119, 175, 40). For integer values x, y, h and 0 < x < y
< 1 000 000, how many triplets (x,y,h) produce integer solutions for
w?