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ABCDisatrapeziumin which AR]I CD and Al 2CD. If its diagonolintersect each other at O, find the ratio of areas o trianglea AOB aneCODCu |
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Answer» given: ABCD is a trapezium with AB||CD.......(1)and AB = 2 CD......(2) In the triangles AOB and COD; ∠DOC = ∠ BOA [vertically opposite angles are equal]∠ CDO = ∠ ABO [alternate interior angles ]∠ DCO = ∠ BAO thus Δ AOB ≈ Δ COD. by the similarity rule, the ratio of the areas of the similar triangles is the ratio of the square of corresponding sides.thereforearea(Δ AOB) : area(Δ COD)=AB^2:CD^2area(Δ AOB) : area(Δ COD)=(2CD)^2:CD^2area(Δ AOB) : area(Δ COD)=4CD^2:CD^2area(Δ AOB) : area(Δ COD) = 4 : 1. it is of herons formula |
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