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KVPY2011MathematicsProperties of Triangles

Let ABC be a triangle with B =90^ . Let AD be the bisector of A with D on BC . Suppose AC =6 ~cm and the area of the triangle ADC is 10 ~cm ² . Then the length of BD in cm is equal to

Options

  1. A3 5
  2. B3 10
  3. C5 3
  4. D10 3

Correct answer

D. 10 3

Step-by-step solution

From angle bisector theorem array l r 6 = p q q r=6 p ...(1) array Area of ADC =10 ~cm ² array l 1 2 ( DC )( AB )=10 1 2 ( q )( r )=10 q r =20 array From (1) array l 20=6 p p = 20 6 = 10 3 array

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