Question 1012965
I agree with Theo, and I believe there is some part of the problem that got lost in translation.
The phrase "Find the lengths of the short and long diagonals" tells me that two diagonals of different length are expected.
That tells me that your parallelogram must be a special kind of parallelogram.
It is not just any parallelogram, possibly a rectangle or a square,
because the two diagonals in a rectangle have the same length.
There is {{{1}}} solution if it is a rectangle, and it is easy to find.
There is {{{1}}} solution if it is a rhombus, and it is relatively easy to find.
If the there are longer and shorter sides, and acute and obtuse angles,
the parallelogram is neither a rectangle nor a rhombus,
and you have {{{infinity}}} of solutions to the problem.
 
Here is how your problem should read:
The area and the perimeter of a parallelogram shown below are 2000 sq. m. and 240 m., respectively. Find the lengths of the short and long diagonals.
{{{drawing(600,200,-60,60,-20,20,
green(triangle(-57.42,0,0,-17.42,0,17.42)),
green(triangle(-57.42,0,57.42,0,0,17.42)),
green(rectangle(0,0,2,2)),
line(-57.42,0,0,17.42),line(57.42,0,0,17.42),
line(-57.42,0,0,-17.42),line(57.42,0,0,-17.42)
)}}} (or maybe the rhombus was tilted so one side would be "horizontal").
The little square in the middle, tells you that the diagonals are perpendicular.
It also tells you that it is a rhombus, and more importantly,
it gives you an easy way to calculate the diagonals.
Let me name a couple variables, and show you how to solve that solvable problem.
{{{drawing(600,200,-60,60,-20,20,
green(triangle(-57.42,0,0,-17.42,0,17.42)),
green(triangle(-57.42,0,57.42,0,0,17.42)),
green(rectangle(0,0,2,2)),locate(-28.7,8.71,s),
locate(-29,0,green(a)),locate(28.5,0,green(a)),
locate(0.2,9.5,green(b)),locate(0.2,-8,green(b)),
rectangle(-57.42,-17.42,57.42,17.42),
line(-57.42,0,0,17.42),line(57.42,0,0,17.42),
line(-57.42,0,0,-17.42),line(57.42,0,0,-17.42)
)}}} {{{system(side=s=sqrt(a^2+b^2),perimeter=4s=240,area=2ab=2000)}}}
{{{system(4sqrt(a^2+b^2)=240,2ab=2000)}}}--->{{{system(sqrt(a^2+b^2)=240/4=60,2ab=2000)}}}--->{{{system(a^2+b^2=60^2=3600,2ab=2000)}}}--->{{{system(a^2+b^2+2ab=3600+2000=5600,ab=2000/2)}}}--->{{{system((a+b)^2=5600,ab=1000)}}}--->{{{system(a+b=sqrt(5600)=20sqrt(14),ab=1000)}}}
Where do we go from here?
There is more than one way to solve that system for {{{a}}} and {{{b}}} , but
we know that the solutions we look for are the solutions to {{{x^2-(a+b)x+ab=0}}} ,
so we solve {{{x^2-20sqrt(14)+1000=0}}}
by using the quadratic formula or by completing the square,
to find {{{x=10sqrt(14) +- 20}}} .
So, the length of the diagonals is
{{{2a=2(10sqrt(14)+20)=20sqrt(14)-40=about114.833}}} for the longer diagonal, and
{{{2b=2(10sqrt(14)-20)=20sqrt(14)-40=about34.833}}} for the shorter diagonal. 
 

I was going to do something similar to Theo's tabulation,
resorting to the Microsoft Excel spreadsheet program
to create a table showing different parallelograms that met the conditions in the problem,
and calculating the length of their diagonals,
but unless it is a rectangle or a rhombus,
it is not fun.
For the rectangle found by Theo, both diagonals are the same length, in meters,
{{{sqrt(100^2+20^2)=sqrt(104000)=20sqrt(26)=about101.98}}} (rounded).
Just finding {{{2}}} parallelograms with different lengths diagonals would do.