question_answer

ABCD is a trapezium with AD and BC parallel sides. E is a point on BC. The ratio of the area of ABCD to that of \[\Delta AED\]is                                                                                      [SSC (CGL) Mains 2014]

A) \[\frac{\overline{AD}}{\overline{BC}}\]                          

B) \[\frac{\overline{BE}}{\overline{EC}}\]

C)  \[\frac{\overline{AD}+\overline{BE}}{\overline{AD}+\overline{CE}}\]                 

D) \[\frac{\overline{AD}+\overline{BC}}{\overline{AD}}\]

Correct Answer: D

Solution :

ABCD is a trapezium with parallel sides \[AD||BC\]

\[\therefore \]Area of ABCD trapezium \[=\frac{1}{2}\times (AD+BC)\times h\]

Area of \[\Delta AED=\frac{1}{2}\times AD\times h\]

\[\therefore \]\[\frac{\text{Area}\,\,\text{of}\,\,ABCD}{\text{Area}\,\,\text{of}\,\,\Delta AED}=\frac{\frac{1}{2}\times (AD+BC)\times h}{\frac{1}{2}\times AD\times h}\]

\[=\frac{AD+BC}{AD}=\frac{\overline{AD}+\overline{BC}}{\overline{AD}}\]