Final answer:
Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of BD. By substituting the known values into the formula for the area of a rhombus, we can solve for BD. The length of BD is 12 cm.
Step-by-step explanation:
Since ABCD is a rhombus, the diagonals bisect each other at right angles. This means that AC and BD are perpendicular to each other. Given that AC is 8 cm, we can use the Pythagorean theorem to find the length of BD.
Let's denote BD as x. Using the property of diagonals in a rhombus, we can form two right triangles with AC and BD as their hypotenuses. The area of a rhombus is given by (AC * BD) / 2.
Therefore, we have (8 * x) / 2 = 48.
Simplifying the equation, we get 4x = 48.
Dividing both sides by 4, we find that x = 12.
The length of BD is
12 cm
.