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Let ABC be a triangle with angleB=90^(@...

Let ABC be a triangle with ` angleB=90^(@)`. Let AD be the bisector of ` angleA` with D on BC. Supose AC = 6 cm and the area of the triangle ADC is 10 `cm^(2)` . Then the length of BD in cm is equal to

A

`3/5`

B

`3/10`

C

`5/3`

D

`10/3`

Text Solution

Verified by Experts

The correct Answer is:
D

From angle bisector theorem
`r/6 = p/q`
` q r=6 p …(1)`
Area of ` DeltaADC = 10 cm^(2)`
`1/2 (DC)(AB)=10`
`1/2 (q)(r)=10`
`q r=20`
From (1)
` rArr 20 =6 p`
`p=(20)/6=(10)/3`
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