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Question

ABCD is a trapezium in which ABDC and AB=2DC. O is the point of intersection of the diagonals. The ratio of the areas of AOB and COD is:

A
1:2
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B
2:1
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C
4:1
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D
1:4
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Solution

The correct option is C 4:1
Given, AAB=2CD ....(1)
In s AOB and COD
AOB=COD (vert. opp. s)
OAB=DCO (DCAB, alt. s are equal)
AOBCOD (AA similarity)
ar(AOB)ar(COD)=AB2CD2 {Ratio of areas of two similar s is equal to the ratio of the squares of the corresponding sides}
=(2CD)2CD2=4CD2CD2=41. ....From (1)
855983_283230_ans_8676dd85818748a781ed32946ee1e62b.png

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