ABC is a right angled triangle with the right angle at vertex B. BD is the altitude through B. given BD =12 cm and AD =9 cm .find the length of BC
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Answer:
Correct option is B)
In △ABC and △DBA,
∠B is common
∠CAB=∠BDA=90
∘
⇒ △ABC∼△DBA
⇒
AC
AB
=
DA
DB
⇒
DA
DB
=
4
3
⇒ AD=
3
4
DB (i)
In △ABD and △ADC,
∠DAB=∠ACD (Third angles of similar △s ABC and DBA)
∠ADB=∠ADC=90
∘
∴
AC
AB
=
CD
AD
=
4
3
⇒AD=
4
3
CD (ii)
From (i) and (ii)
3
4
DB=
4
3
CD⇒
CD
BD
=
4
3
×
4
3
=
16
9
.
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