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Let A B C be a triangle with /B=90^0 . L...

Let `A B C` be a triangle with `/_B=90^0` . Let AD be the bisector of `/_A` with D on BC. Suppose AC=6cm and the area of the triangle ADC is `10c m^2dot` Find the length of BD.

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From angle bisector theorem,

`(r)/(6) = (p)/(q)`
`rArr qr = 6p` ..(1)
Now, area of `DeltaADC = 10 cm^(2)`
`(1)/(2) (DC) (AB) = 10`
`(1)/(2) (q) (r) = 10`
`qr = 20`
From (1), 20 = 6p
`rArr p = (20)/(6) = (10)/(3)`
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