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

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

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Answer 1 · 2017-01-07T05:03:19

$A B = 6$ $AB=6$

Explanation:

As $A D$ $AD$ is drawn perpendicular to $B C$ $BC$ 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 $AB=6$

Answer 2 · 2017-01-07T05:04:21

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

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

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

$=>AB=sqrt36cm=6cm$

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

2 Answers

Explanation:

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