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