The perimeter of a rhombus is 20 cm. The length of one of its diagonals is 6 cm. What is the length of the other diagonal?

The perimeter of a rhombus is 20 cm.

the perimeter of a rhombus = 4$$\times$$ length of the side

20 = 4$$\times$$ length of side

length of side = 5 cm

Let's assume that d1 and d2 are the two diagonals.

length of side = $$\frac{1}{2}\ \times\ \sqrt{\ \left(d1\right)^2\ +\ \ \left(d2\right)^2}$$

5 = $$\frac{1}{2}\ \times\ \sqrt{\ \left(d1\right)^2\ +\ \ \left(d2\right)^2}$$

10 = $$ \sqrt{\ \left(6\right)^2\ +\ \ \left(d2\right)^2}$$

100 = 36 + $$\left(d2\right)^2$$

$$\left(d2\right)^2$$ = 100-36 = 64

length of the other diagonal = d2 = 8 cm