1
Question
In Fig. 7.139, ∠ABC=90∘ and BD⊥AC. If BD = 8 cm and AD = 4 cm, find CD.
In Fig. 7.139, ∠ABC=90∘ and BD⊥AC. If BD = 8 cm and AD = 4 cm, find CD.
Open in App
Solution
In 
ABC and 
ADB
ABC =
ADB (right angle)
BAD = 
BAC (common angle)
180 - (
ABC + 
BAC ) = 180 - (
ADB +
BAD )
DBA = 
BCA (proved)
Hence both the triangles are similar.
In 
ADB
BD
+ DA
= AB
16+64 = AB
AB = 4
As we know
(Corresponding sides of similar triangles)
Therefore, CD = 8
- 4 cm
In ABC and ADB
ABC = ADB (right angle)
BAD = BAC (common angle)
180 - (ABC + BAC ) = 180 - ( ADB +BAD )
DBA = BCA (proved)
Hence both the triangles are similar.
In ADB
BD + DA = AB
16+64 = AB
AB = 4
As we know
(Corresponding sides of similar triangles)
Therefore, CD = 8 - 4 cm
Suggest Corrections
0
