The perimeter of a rhombus is 40 cm and the length of one of its diagonals is 12 cm then the length of the other diagonal is

16 cms.

Step-by-step explanation:

The length of each side = 40 / 4 = 10 cm (as the 4 sides of a rhombus are congruent).

If we draw the other diagonal we form 4 right angled triangles (another property of the rhombus - diagonals bisect each other at tight angles. ).

The side of the rhombus is the hypotenuse of the right triangle.

So if we consider one triangle:

10^2 = 6^2 + x^2   where x is half the length of the other diagonal.

x^2 = 10^2 - 6^2

x^2 = 100 - 36 = 64

x = 8 cm.

So the diagonal is 16 cms long.

step-by-step explanation: