question_answer

If PQRS be a rhombus, PR is its smallest diagonal and \[\angle \mathbf{PQR}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\], find length of a side of the rhombus when \[\mathbf{PR}=\mathbf{6}\]cm.

A)  6 cm   

B)  3 cm

C)  \[6\sqrt{2}\]cm                         

D)  \[3\sqrt{3}\]cm

Correct Answer: A

Solution :

(a): \[\angle PQR={{60}^{{}^\circ }}\] \[PQ=QR\] \[\therefore \]\[\angle QPR=\angle QRP={{60}^{{}^\circ }}\] \[\therefore \]\[\Delta PQR\] is an equilateral triangle.