Question

65) Find the perimeter of a rectangle whose breadth is 9cm and diagonal is 41cm.
The diagonal of rhombus measure 50cm and 48cm. Find its perimeter​

Answer 1

Answer:

Question 1 -:

Perimeter of the rectangle = 98 cm

Question 2 -:

Perimeter of the Rhombus = 138.6 cm

Step-by-step explanation:

Given :

Question 1 -:

Breadth of the rectangle = 9 cm

Diagonal of the rectangle = 41 cm

Question 2 -:

Diagonal of the Rhombus = 50 cm and 48 cm

To find :

Question 1 -:

Perimeter of the rectangle

Question 2 -:

Perimeter of the Rhombus

Concept :

Question 1 -:

We have to first find the length of the rectangle .

Using the Pythagoras theorem to find the length -:

Let,

AB = Length

AD = Breadth

AC = Diagonal

$\boxed{\sf{{AD}^{2}+{AB}^{2}={AC}^{2}}}$

After that to find the perimeter of the rectangle use this formula -:

$\boxed{\sf{P=2(L+B)}}$

Where,

P = Perimeter

L = Length

B = Breadth

Question 2 -:

We have to first find the side of the Rhombus .

Using Pythagoras theorem -:

Let ,

AB = Side of the Rhombus

AC = ½ of 50 cm

=> 25 cm = OA

BD = ½ of 48 cm

=> 24 cm = OB

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

After that to find the perimeter of the Rhombus use this formula -:

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

Where,

A = Area of the Rhombus

a = Side

Solution :

Question 1 -:

Length -:

$:\implies\sf{{9cm}^{2}+{AB}^{2}={41cm}^{2}}$

$:\implies\sf{AB=\sqrt{(41cm\times41cm)-(9cm\times9cm)}}$

$:\implies\sf{AB=\sqrt{1681cm-81cm}}$

$:\implies\sf{AB=\sqrt{1600}}$

$:\implies\sf{AB=40cm}$

Perimeter of the rectangle -:

$:\implies\sf{P=2(40cm+9cm)}$

$:\implies\sf{P=2(49cm)}$

$:\implies\sf{P=98cm}$

So , the perimeter of the rectangle is 98 cm .

Question 2 -:

Side of the Rhombus -:

$:\implies\sf{{AB}^{2}={25cm}^{2}+{24cm}^{2}}$

$:\implies\sf{AB=\sqrt{(25cm\times25cm)+(24cm\times24cm)}}$

$:\implies\sf{Ab=\sqrt{625cm+576cm}}$

$:\implies\sf{AB=\sqrt{1201cm}}$

$:\implies\sf{AB=34.65cm(approx)}$

Perimeter of the Rhombus -:

$:\implies\sf{P=4\times34.65cm(approx)}$

$:\implies\sf{P=138.6cm(approx)}$

So , the perimeter of the Rhombus is 138.6 cm (approx) .