Question

In figure angle 90 degree AD perpendicular BC if BD =2cm and CD=8 find AD​

Answer 1

Answer:

From the figure, consider △ABC,

So, ∠A=90  

∘

 

And AD⊥BC

∠BAC=90  

∘

 

Then, ∠BAD+∠DAC=90  

∘

 … [equation (i)]

Now, consider △ADC

∠ADC=90  

∘

 

So, ∠DCA+∠DAC=90  

∘

 … [equation (ii)]

From equation (i) and equation (ii)

We have,

∠BAD+∠DAC=∠DCA+∠DAC

∠BAD=∠DCA … [equation (iii)]

So, from △BDA and △ADC

∠BDA=∠ADC … [both the angles are equal to 90  

∘

]

∠BAD=∠DCA … [from equation (iii)]

Therefore, ∠BDA∼∠ADC

BD/AD=AD/DC=AB/AC

Because, corresponding sides of similar triangles are proportional

BD/AD=AD/DC

By cross multiplication we get,

AD  

2

=BD×CD

AD  

2

=2×8=16

AD=  

16

​

 

AD=4.

Answer 2

Answer:

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