SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-10
question_answer
ABCD is a trapezium in which AB | | CD and AB = 2 CD. Its diagonals intersect each other at O, then the ratio of the areas of the triangles AOB and COD is :
A)1: 2
B)2: 1
C)4: 1
D)1: 4
Correct Answer:
C
Solution :
Let PQ be the perpendicular distance between the two parallel sides AB and CD. So, \[\frac{area\,\,of\,\Delta \,AOB}{area\,\,of\,\Delta \,COD}\] \[=\,\,\,\frac{\frac{1}{2}AB\times OP}{\frac{1}{2}CD\times OQ}[\because \,OP=\,2OQ]\] \[=\frac{2CD\times 2OQ}{CD\times OQ}=\frac{4}{1}\]