Question

If the diagonals of a rhombus are 12cm and 5cm find the perimeter of the rhombus

Answer 1

Answer:

26 cm

Step-by-step explanation:

The formula for Rhombus Perimeter is given by:

P = 2 x square root of ( d1^2 + d2^2)

Here d1 = 12 and d2 = 5

So,

P = 2 x square root of ( 12^2 + 5^2)

  = 2 x square root of ( 144 + 25)

  = 2 x square root of ( 169 )

  = 2 x 13

  = 26

 

Answer 2

Given : The diagonals of a rhombus are 12cm and 5cm.

To find : The perimeter of the rhombus.

Solution :

The perimeter of the rhombus is

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the perimeter of the given rhombus)

First of all, we have to calculate the length of the side of the rhombus. (all 4 sides are equal, in case of a rhombus)

Now, the diagonals of the rhombus are perpendicular bisectors of each other. Furthermore, if we apply the Pythagoras theorem, we get -

(Side of the rhombus)² = (First diagonal/2)² + (Second diagonal/2)²

Or,

(Side of the rhombus)² = (12/2)² + (5/2)²

Or,

(Side of the rhombus)² = 36 + 6.25

Or,

(Side of the rhombus)² = 42.25

Or,

Side of the rhombus = √42.25 = 6.5 cm

Now,

The perimeter of the rhombus = 4 × side

Or,

The perimeter of the rhombus = 4 × 6.5 = 26 cm

Hence, the perimeter of the rhombus is 26 cm