in the given figure angle A=90 degree,AD perpendicular BC If BD=2cm and CD=8cm,find AD - Math - Triangles

Question

in the given figure angle A=90 degree,AD perpendicular BC If
BD=2cm and CD=8cm,find AD

Manbar Singh · Accepted Answer

In ∆ ABC, we have, ∠A = 90°
Also, AD⊥BC
Now,In ∆ABC, we have,∠BAC = 90°⇒∠BAD + ∠DAC = 90°  
1In ∆ADC, we have,∠ADC = 90°So, ∠DCA + ∠DAC = 90°  
2from 1 and 2, we have∠BAD + ∠DAC = ∠DCA + ∠DAC ⇒∠BAD = ∠DCA   
3In ∆BDA and ∆ADC,  ∠BDA = ∠ADC   90° each  ∠BAD = ∠DCA    proved above  so, ∆BDA ~ ∆ADC  AA similarity⇒BDAD = ADDC = ABAC Corresponding sides of similar ∆'s are proportional⇒BDAD = ADDC⇒AD2 = BD × CD⇒AD2 = 2 × 8 = 16⇒AD = 4 cm

in the given figure angle A=90 degree,AD perpendicular BC.If BD=2cm and CD=8cm,find AD