Question

diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
​

Answer 1

Answer:Given: Diagonals AC=30cm and DB=16cm.

Since the diagonals of the rhombus bisect at right angle to each other.

Therefore, OD=  

2

DB

​  

=  

2

16

​  

=8cm

and OC=  

2

AC

​  

=  

2

30

​  

=15cm

Now, In right angle triangle DOC,

(DC)  

2

=(OD)  

2

+(CO)  

2

 

⇒(DC)  

2

=(8)  

2

+(15)  

2

 

⇒(DC)  

2

=64+225=289

⇒DC=  

289

​  

=17cm

Perimeter of the rhombus=4× side

=4×17=68cm

Thus, the perimeter of rhombus is 68 cm.

Step-by-step explanation:

Answer 2

Given:-

• Diagonals of rhombus 16 cm and 30 cm.

To find:-

• Perimeter of rhombus.

$\huge \tt \:☃\: Solution$

• We know that , diagonals of rhombus bisect each other and forms 90°.

View the diagram.

• We need side of rhombus for perimeter.

So,

In triangle AOD,

AD is Hypotenuse and AD is side of rhombus.

Formula used:-

Pythagoras theorem that is,

☘(Hypotenuse)² = (Base)² + (Perpendicular)²

• Base = DO = 15cm and perpendicular = AO= 8 cm

Put that values,

⇒(AD)² = (15)² + (8)²

⇒(AD)² = 225 + 64

⇒(AD)² = 289

⇒AD = √289

⇒AD = 17

So, One side of rhombus is 17 cm.

We know that,

All sides of rhombus are same.

☘ Perimeter of rhombus = 4a

In which a is side.

⇒4 × 17

⇒68 cm

Thus, Perimeter of rhombus is 68 cm.