Question

In triangle ABC,angle c=90 and CD perpendicular to AB,CD=h,BC=a,CA=b,AB=c,prove that,1/h^2=1/a^2+1/b^2

Answer 1

Step-by-step explanation:

Let CD⊥AB. Then, CD=p

∴ Area of ΔABC=

2

1

(Base×Height)

=

2

1

(AB×CD)=

2

1

cp

Also,

Area of ΔABC=

2

1

(BC×AC)=

2

1

ab

∴

2

1

cp=

2

1

ab

⇒cp=ab

(ii) Since ΔABC is a right triangle, right angled at C.

∴AB

2

=BC

2

+AC

2

⇒c

2

=a

2

+b

2

⇒(

p

ab

)

2

=a

2

+b

2

[∵cp=ab⇒c=

p

ab

]

⇒

p

2

a

2

b

2

=a

2

+b

2

⇒

p

2

1

=

b

2

1

+

a

2

1

⇒

p

2

1

=

a

2

1

+

b

2

1