One internal angle of a rhombus of side 12cm is 120
∘
. What is the length of its longer diagonal?
- A6
3
cm - B12
2
cm - C6
2
cm - D12
3
cm
Solution & Step-by-step Explanation
Let the rhombus be ABCD with side a=12cm and ∠BAD=120
∘
.
The diagonals of a rhombus bisect each other perpendicularly and bisect the internal angles.
Therefore, the diagonal AC bisects ∠BAD, making ∠OAD=60
∘
(where O is the intersection point of the diagonals).
In right-angled triangle △AOD:
sin(60
∘
)=
AD
OD
2
3
=
12
OD
OD=6
3
cm
The length of the longer diagonal BD is:
BD=2×OD=2×6
3
=12
3
cm
∘
.
The diagonals of a rhombus bisect each other perpendicularly and bisect the internal angles.
Therefore, the diagonal AC bisects ∠BAD, making ∠OAD=60
∘
(where O is the intersection point of the diagonals).
In right-angled triangle △AOD:
sin(60
∘
)=
AD
OD
2
3
=
12
OD
OD=6
3
cm
The length of the longer diagonal BD is:
BD=2×OD=2×6
3
=12
3
cm