Question

in ∆ABC,b-d-c and bd=8,bc=20,find the following ratio:

1)A(∆ABD)
_______
A(∆ADC)



2)A(∆ABD)
_______
A(∆ABC)



3)A(∆ADC)
_______
A(∆ABC)


please solve I will mark brilianist

Answer 1

According to the question, there is a triangle ABC with a point D on BC such that it divides the side BC in the ratio 8:(20-8) = 8 : 12

Now, Since the side is divided in the ratio of 8 : 12 , The area of ABD : ADC will also be divided in the ratio 8 : 12 by angle bisector theorem, let them be 8x and 12x. The total area will be 20x.

ABD : ABC = 8x : 20x = 8 : 20

Similarly ADC : ABC = 12 : 20

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