Question

ln Triangle ABC D is a point on AC .If BD=8cm BC=20cm CD=16cm and Angle CBD= angle CAB find the perimeter of triangle ABD .​

Answer 1

Given :  ΔABC D is a point on AC . BD=8cm BC=20cm CD=16cm and ∠CBD= ∠CAB

To Find : perimeter of triangle ABD .​

Solution:

Compare Δ CAB & Δ CBD

∠C = ∠C  ( Common angle)

∠CAB  = ∠CBD  ( given )

If two angles are equal then third angle is also equal

Hence  Δ CAB ≈ Δ CBD  

=> AC/BC  = AB/ BD   = BC/CD

=> AC/20 = AB/8  =  20/16

=> AC/20 = AB/8  =  5/4

=> AB = 10 cm

& AC = 25 cm

perimeter of triangle ABD .​ = AB + BD  + AD

= 10 + 8 +  ( AC - CD)

= 18  + ( 25 - 16)

= 18 + 9

= 27 cm  

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