Right triangles with sides in terms of x

All lengths are in centimetres.

1. A right-angled triangle has sides \(x\), \(x+7\) and \(x+8\), where \(x+8\) is the hypotenuse. Find \(x\) and the area of the triangle.[4]
2. Another right-angled triangle has sides \(y\), \(y+1\) and \(y+3\), where \(y+3\) is the hypotenuse. Show that \(y=2+2\sqrt{3}\) and explain why this triangle cannot have all three sides of integer length.[3]