question_answer

The two adjacent sides of a parallelogram are 4 cm and 9 cm. The ratio of its altitudes is

A) 21 : 22                        

B) 4 : 9

C) 16 : 81                        

D) 11 : 37

Correct Answer: B

Solution :

    Let ABCD be the given parallelogram. If\[\angle DAB\]equal to\[\theta \], then\[\angle DCB\]will also be equal to\[\theta \]. DM and DN are the two altitudes. Now, in right angled triangle AMD, \[DM=4\,\,\sin \theta \]                                    ...(1) Similarly, in right angled triangle CND, \[DN=9\,\,\sin \theta \]                                     ...(2), From equations (1) and (2), \[\frac{DM}{DN}=\frac{4\sin \theta }{9\sin \theta }=\frac{4}{9}.\]