ABC is a right angle triangle. AD is drawn perpendicular to BC. If BC = 9cm, BD = 4 cm then find AB?

2 Answers
Jan 7, 2017

AB=6AB=6

Explanation:

As ADAD is drawn perpendicular to BCBC in right angled DeltaABC, it is apparent that DeltaABC is right angled at /_A as shown below (not drawn to scale).
enter image source here
As can be seen /_B is common in Delta ABC as well as DeltaDBA (here we have written two triangles this way as /_A=/_D, /_B=/_B and /_C=/_BAD) - as both are right angled (obviously third angles too would be equal) and therefore we have

Delta ABC~~DeltaDBA and hence

(BC)/(AB)=(AB)/(BD)=(AC)/(AD)..............(1)

therefore, we have (BC)/(AB)=(AB)/(BD) or

AB^2=BCxxBD=9xx4=36

Hence AB=6

Jan 7, 2017

drawn

Given that DeltaABC is right angled and AD is drawn perpendicular to BC . So /_BAC is right angle.

Given BC = 9cm and BD =4cm-> CD = BC-BD=5cm

In Delta ABC and Delta ABD

  • /_ABD=/_ABC

  • /_ADB=/_BAC= "right angle"

  • /_BAD=/_ACD ("remaining")

So Delta ABC and Delta ABD are similar

Hence

(AB)/(BC)=(BD)/(AB)

=>AB^2=BDxxBC=4xx9=36

=>AB=sqrt36cm=6cm