Given:
- Parallelogram ABCD
- AC = 16 cm
- AB = 10 cm
- Diagonals of parallelogram ABCD bisect each other at right angles

To Find:
- Length of diagonal DB

Solution:

Step 1: Identify the Properties of a Parallelogram
- Opposite sides of a parallelogram are equal in length
- Opposite angles of a parallelogram are equal in measure
- Diagonals of a parallelogram bisect each other

Step 2: Identify the Given Information
- AC = 16 cm
- AB = 10 cm
- Diagonals of ABCD bisect each other at right angles

Step 3: Use the Given Information to Find Additional Information
- Since the diagonals of ABCD bisect each other, we can conclude that the diagonals divide the parallelogram into four congruent triangles.
- Let's consider one of these triangles, triangle ADB.

Step 4: Apply the Properties of a Parallelogram
- In triangle ADB, AD is the base and AB is the height.
- The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.
- Therefore, the area of triangle ADB is: Area = 1/2 * AD * AB.

Step 5: Calculate the Area of Triangle ADB
- Since triangle ADB is congruent to triangle BDC (due to the properties of a parallelogram), the area of triangle BDC is also 1/2 * AD * AB.

Step 6: Calculate the Length of Diagonal DB
- The length of diagonal DB is equal to the sum of the bases of triangles ADB and BDC.
- Therefore, the length of diagonal DB = AD + AD = 2 * AD

Step 7: Find the Length of AD
- Since the diagonals of ABCD bisect each other at right angles, we can use the Pythagorean Theorem to find the length of AD.
- The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- In triangle ACD, AC is the hypotenuse and AD is one of the legs.
- Using the Pythagorean Theorem: AC^2 = AD^2 + CD^2

Step 8: Calculate the Length of AD (continued)
- Since ABCD is a parallelogram, opposite sides are equal in length.
- Therefore, CD = AB = 10 cm.
- Substituting the known values into the Pythagorean Theorem: (16 cm)^2 = AD^2 + (10 cm)^2

Step 9: Solve the Equation
- Solving the equation: 256 cm^2 = AD^2 + 100 cm^2
- Subtracting 100 cm^2 from both sides: AD^2 = 156 cm^2
- Taking the square root of both sides: AD = √156 cm
- Simplifying the square root: AD ≈