Question

in a parallelogram the adjacent sides are 39 cm and 25 cm respectively and the diagonals of the parrallelogram are 34 cm in length
. find are of the parallelogram.

Answer 1

There is a 3-dimensional version of this problem:

Does a rational box exist? (MathWorld calls it the perfect cuboid problem.)

That is, is there a box with integer sides a, b, and c, with each face diagonal integral, and with body diagonal integral?

So, a, b, and c are integers, and these four equations are solvable in integers:

a² + b² = d²,

a² + c² = e²,

b² + c² = f²,

a² + b² + c² = g².

People have come one equation short.