Question

ABC is a right triangle, right angled at C. let BC=a,CA=b,AB=c and let p be the length of the perpendicular frm C on AB. Prove that 1)cp=ab 2) 1/p²=1/a² + 1/b²
please explain with attachment​

Answer 1

Answer:

ANSWER

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

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