Find the length of the sides of the right angled triangle?

If your hypotenuse is h, then the base is h - 1 and the height is (h - 3)/2. Use the Pythagorean theorem to find h:

hyp^2 = base^2 + alt^2

h^2 = (h - 1)^2 + [(h - 3)/2]2

h^2 = h^2 - 2h + 1 + (h^2 - 6h + 9)/4

4h^2 = 4h^2 - 8h + 4 + h^2 - 6h + 9

0 = h^2 - 14h + 13

0 = (h - 13)(h - 1)

h = 13, 1

h can't be 1, since the base would be 0 if that were the case. Thus, the hypotenuse is 13, the base is 12, and the altitude is 5.