Mathematics
PQRS is a rhombus in which PQ = 6 cm and ∠PQR = 120°. The length of the diagonal QS is :
6 cm
7 cm
8 cm
11 cm
Rectilinear Figures
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Answer
In triangle PQS,
PQ = PS = 6 cm (because all sides of a rhombus are equal).
Therefore, the base angles are equal:
∠PQS = ∠PSQ.
∠PQR = ∠PSR = 120° [Opposite angles of a rhombus are equal]
∠PQR + ∠QPS = 180° [Consecutive angles are supplementary]
∠QPS = 180° - 120°
∠QPS = 60°.
In triangle PQS,
∠QPS + ∠PQS + ∠PSQ = 180°
60° + 2∠PQS = 180°
2∠PQS = 180° - 60°
2∠PQS = 120°
∠PQS = 60°.
Since all three angles (∠QPS, ∠PQS, and ∠PSQ) are 60°, △PQS is an equilateral triangle.
PQ = PS = QS = 6 cm.
Hence, option 1 is the correct option.
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