Question

In a triangle ABC right angled at B and BD perpendicular to AC if AD=5cm CD=6cm find BD AB

Answer 1

Answer:

Let AB = x, BD = y and BC = z.

From triangle ABC,

{x}^{2}  +  {z}^{2}  =  {(4 + 5)}^{2}  = 81 -  - (1)

From triangle ADB,

{x}^{2}  =  {y}^{2}  + 16 -  -  - (2)

From triangle BDC,

{z}^{2}  =  {y}^{2}  + 25 -  -  - (3)

Substituting (2) and (3) in (1),

( {y}^{2}  + 16) + ( {y}^{2}  + 25) = 81 \\  {y}^{2}  = 20 -  -  - (4) \\ y = 2 \sqrt{5}  

Substituting (4) in (2),

{x}^{2}  = 20 + 16 \\ x = 6

Thus BD = 2√5; AB = 6