The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is ______.

#### Options

9 cm

10 cm

8 cm

20 cm

#### Solution

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is **1****0 cm**.

**Explanation: **

We know that,

A rhombus is a simple quadrilateral whose four sides are of same length and diagonals are perpendicular bisector of each other.

We get,

AC = 16 cm and BD = 12 cm

∠AOB = 90°

∵ AC and BD bisects each other

AO = `1/2` AC and BO = `1/2` BD

Then we get,

AO = 8 cm and BO = 6 cm

Now, In right angled ∆AOB

Using the Pythagoras theorem,

We have,

AB^{2} = AO^{2} + OB^{2}

AB^{2} = 8^{2} + 6^{2}

= 64 + 36

= 100

∴ AB = `sqrt(100)` = 10 cm

We know that the four sides of a rhombus are equal.

Therefore, we get,

One side of rhombus = 10 cm.