The smallest right-angled triangle where the lengths of all the sides are integers, has sides of length 3, 4 and 5 units. This triangle has an area of 6 square units and a perimeter of 12 units:
- How many right-angled triangles are there with sides that are all integers less than 100 units?
- In how many of these triangles is the area one half of the perimeter?
