Question

in a triangle ABC right angled at B, AB = X cm, BC=(x+1) cm and CA=(x+2) cm. The area of triangle.

Answer 1

I hope this helped you a lot

Answer 2

Answer:

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Step-by-step:-

AB  

2

=AC  

2

−BC  

2

=4−1=3

AB=  

3

​  

 

ar( Δ ABC) =  

2

1

​  

×AB×BC

=  

2

1

​  

×  

3

​  

×1×=  

2

3

​  

 

​  

 

Also ar( Δ ABC) =  

2

1

​  

×BD×AC

=  

2

1

​  

×BD×2

⇒  

2

3

​  

 

​  

=BD

Consider ΔBDF & ΔACB    

∠BFD=∠ABC=90  

o

 

∠DEC+∠DCB=90  

o

=∠BAC+∠BCA

∠DBF+∠DCB=∠BAC+∠BCD

∠DBF+∠BACΔBDF∼ΔACB (AA axiom of similarity).  

⇒  

CB

DF

​  

=  

BD

​  

AC=  

AB

BF

​  

 

⇒  

1

DF

​  

=  

4

3

​  

 

​  

=  

3

​  

 

BF

​  

 

⇒DF=  

4

3

​  

 

​  

 & BF=  

4

3

​  

 

ar(BEDF)=BF×DF=  

4

3

​  

×  

4

3

​  

 

​  

=  

16

3  

3

​  

 

​