The perimeter of a rhombus is 40 cm, and the length of one of its diagonals is 16 cm.

To find the length of the other diagonal of the rhombus, we can use some properties of rhombuses:

1. The perimeter of a rhombus is given by the formula: (P = 4s), where (s) is the length of a side. In this case, we know the perimeter is 40 cm, so:

[

4s = 40 implies s = 10 text{ cm}

]

2. The diagonals of a rhombus bisect each other at right angles (90 degrees). Let’s denote the diagonals as (d_1) and (d_2). Given (d_1 = 16) cm, it will be halved to (8) cm for our calculations.

3. We can represent each half of the diagonals related to the sides of the rhombus using the Pythagorean theorem:

[

s^2 = left(frac{d_1}{2}right)^2 + left(frac{d_2}{2}right)^2

]

Substituting the known values:

[

10^2 = 8^2 + left(frac{d_2}{2}right)^2

]

[

100 = 64 + left(frac{d_2}{2}right)^2