Each of the two diagonals and each of the four sides of a rhombus has integer lengths, satisfying the condition: x2 + y2 = 4z2, where x, y are the length of the diagonals and z being the length of each side.
Is the area of the rhombus always divisible by 24?
If so, prove it. Otherwise provide a counter example.
Let x=2a and y=2b
Than a,b,z form a Pythagorian triple .(PT).
A primitive PT has inter alia two features:
- Exactly one of a, b is divisible by 3
- Exactly one of a, b is divisible by 4
So ab is 12*pq.- p,q integers.
The word exactly might be redundant in non primitive PT.
the area of the "integer" rhombus
is always divisible by 24.