Question

A romas of side 10cm has two angles of 60', then the length of the
diagonals of the thombus are​

Answer 1

Answer:

Explanation:

Let ABCD be a rhombus of side 10cm and ∠BAD=∠BCD=60  

o

. Diagonals of parallelogram bisect each other.

So, AO=OC and BO=OD

In right triangle AOB

sin30  

o

=  

AB

OB

​  

 

⇒  

2

1

​  

=  

10

OB

​  

 

⇒ OB=5cm

∴ BD=2(OB)

⇒ BD=2(5)

⇒ BD=10cm

cos30  

o

=  

AB

OA

​  

 

⇒  

2

3

​  

 

​  

=  

10

OA

​  

 

⇒ OA=5  

3

​  

 

∴ AC=2(OA)

⇒ AC=2(5  

3

​  

)

⇒ AC=10  

3

​  

cm

So, the length of diagonals AC=10  

3

​  

cm and BD=10cm

Area of Rhombus =  

2

1

​  

×AC×BD

=  

2

1

​  

×10  

3

​  

×10

=50  

3

​