Question

The area of a rhombus is 25cm² & one of its diagonals is 4cm.  

         Find its perimeter?​

Answer 1

Answer:

Perimeter of the Rhombus = 26.24 cm(approx)

Step-by-step explanation:

Given :

Area of the Rhombus = 25 cm²

One diagonal = 4 cm

To find :

The perimeter of the Rhombus

Concept :

To find the perimeter of the Rhombus use this formula -:

$\boxed{\sf{P=4a}}$

So , we have to first find the side of the Rhombus . And to find the side of the Rhombus we have to use the Pythagoras theorem . And to find it first find the another diagonal of the Rhombus .

So , to find the another diagonal of the Rhombus use this formula -:

$\boxed{\sf{A=\dfrac{1}{2}\times d_{1}\times d_{2}}}$

Where,

A = Area of the Rhombus

$\sf{d_{1}}$ = One diagonal

$\sf{d_{2}}$ = Another diagonal

After that to find the side use the Pythagoras theorem -:

$\boxed{\sf{{AB}^{2}={OA}^{2}+{OB}^{2}}}$

Solution :

Another diagonal of the Rhombus -:

$:\implies\sf{{25cm}^{2}=\dfrac{1}{\cancel{2}}\times\cancel{4}\times d_{2}}$

$:\implies\sf{{25cm}^{2}=2\times d_{2}}$

$:\implies\sf{\cancel{\dfrac{{25cm}^{2}}{2}}=d_{2}}$

$:\implies\sf{12.5cm=d_{2}}$

Side of the diagonal -:

$:\implies\sf{{AB}^{2}={2}^{2}+{6.25}^{2}}$

$:\implies\sf{AB=\sqrt{(2\times2)+(6.25\times6.25)}}$

$:\implies\sf{AB=\sqrt{4+39.0625}}$

$:\implies\sf{AB=\sqrt{43.0625}}$

$:\implies\sf{AB=6.56cm(approx)}$

Perimeter of the Rhombus -:

$:\implies\sf{P=4\times6.56cm(approx)}$

$:\implies\sf{P=26.24cm(approx)}$

So , the perimeter of the Rhombus is 26.24 cm (approx) .

Answer 2

Answer:

Perimeter of the Rhombus = 26.24 cm(approx)

Step-by-step explanation:

Given :

Area of the Rhombus = 25 cm²

One diagonal = 4 cm

To find :

The perimeter of the Rhombus

Concept :

To find the perimeter of the Rhombus use this formula -:

So, we have to first find the side of the Rhombus. And to find the side of the Rhombus we have to use the Pythagoras theorem. And to find it first find another diagonal of the Rhombus.

So, to find another diagonal of the Rhombus use this formula -:

Where,

A = Area of the Rhombus

= One diagonal

= Another diagonal

After that to find the side use the Pythagoras theorem -:

Solution :

Another diagonal of the Rhombus -:

Side of the diagonal -:

Perimeter of the Rhombus -:

So , the perimeter of the Rhombus is 26.24 cm (approx) .

Step-by-step explanation: