The perimeter of rhombus is 20cm. if one of its diagonal is 6cm,then find its area?

If the diagonal is 6 then two sides add to 10. That defines a triangle such that x^2 + y^2 = 36 and x + y = 10.

You have two lines. Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. The lines look like this: www.wolframalpha.com/input/?i=plot+x%5E2+%2B+y%5E2+%3D+36,+x+%2B+y+%3D+10

Since they don't cross, there is no solution.