Question

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

Answer 1

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is 10 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,

AB² = AO² + OB²

AB² = 8² + 6² 

= 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.