question_answer

The parallel sides of a trapezium are p and q respectively. The line joining the midpoints of its non-parallel sides will be:

A)  \[\sqrt{pq}\]                 

B)  \[\frac{2pq}{p+q}\]

C)  \[\frac{(p+q)}{2}\]                   

D)  \[\frac{1}{2}(p-q)\]

Correct Answer: C

Solution :

In \[\Delta \,\,ADC\] M and N are mid-point of AD and BC \[\therefore \,\,\,MO=\frac{q}{2}\] (mid-point theorem) and \[ON=\frac{P}{2}\]             \[\therefore \,\,\,\,\,MO+ON=MN=\frac{p}{2}+\frac{q}{2}=\underline{\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(p+q)}}\]