1.

diagonals of a Trapezium ABCD with ab parallel to dc intersect each other at point o if AB equal to 3 CD find the ratio of their area of triangle ABC and triangle COD​

Answer»

Answer:

9:1

Step-by-step explanation:

Given,

ABCD is a trapezium with AB∣∣CD        .......(1)

And  

AB=3CD            ......(2)

In the triangles AOB and COD,

∠DOC=∠BOA [vertically opposite angles are equal]

∠CDO=∠ABO [alternate interior angles ]

∠DCO=∠BAO  

THUS,

△AOB≈△COD

By the similarity rule, the ratio of the areas of the SIMILAR triangles is the ratio of the square of corresponding sides.

therefore

Area (△AOB): Area (△COD)=AB^2  :CD^2

Area (△AOB):Area (△COD)=(3CD)^2  :CD^2

Area (△AOB):Area (△COD)=9CD^2  :CD^2

Area (△AOB):Area (△COD)=9:1

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