12. Diagonals of a trapezium ABCD with AB || CD intersects at O. If AB = 2CD, find the ratio of
areas of triangles AOB and COD.
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Final Answer : 4: 1
Steps:
1) In AOB & COD,
/AOB = /COD. ( Vertically opposite angles)
/ABO =/ ODC ( Alternate interior angles)
=> AOB similar to COD
2)We know that,
Theorem : The ratio of area of two similar triangles is equal to the square of their corresponding sides.
=> ar( AOB) / ar(COD) = (AB) ^2/(CD) ^2
= (2CD) ^2/(CD) ^2
= 4/1
Therefore, Required Ratio is 4:1
Steps:
1) In AOB & COD,
/AOB = /COD. ( Vertically opposite angles)
/ABO =/ ODC ( Alternate interior angles)
=> AOB similar to COD
2)We know that,
Theorem : The ratio of area of two similar triangles is equal to the square of their corresponding sides.
=> ar( AOB) / ar(COD) = (AB) ^2/(CD) ^2
= (2CD) ^2/(CD) ^2
= 4/1
Therefore, Required Ratio is 4:1
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