Question

AABC is right angled at C. If p is the length of the perpendicular from Cto
AB and a,b,care the length of the sides opposite <A.<B, C respectively then
prove that
po b​

Answer 1

$\huge \purple A \purple N \purple s\purple W \purple e \purple \R :-$

Area of triangle ACB = 1/2ba .............(i)

Also P is the perpendicular distance .

∴ Area = 1/2PC .......................................(ii)

From (i) & (ii) ,

ab = PC .....................................................(iii)

But we know C = √ a^2 + b^2

=> C^2 = a^2 + b^2

Now by (iii) ,

a^2b^2 = P^2C^2 = P^2( a^2 + b^2 )

=> 1/P^2 = a^2 + b^2 / a^2b^2 = 1/b^2 + 1/a^2

=> 1/P^2 = 1/a^2 = 1/b^2

Refer attachment ...