Question

A rhombus of side 12 cm has two angles of 120°

each. Find the length of its

diagonals​

Answer 1

Answer:

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

Answer 2

Answer:

Kindly find the solution in the attached file.

MARK BRAINLIEST!