Login/Sign Up
Home » A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is (a^2/3+b^2/3)^3/2
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is (a^2/3+b^2/3)^3/2
Applications of Derivatives | CBSE | Class 12 | Maths | Miscellaneous | NCERT
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is (a^2/3+b^2/3)^3/2

Let P be a point on the hypotenuse AC of a right triangle ABC such that PL AB =  and PM BC =  and let BAC = MPC = , then in right angled  

AP = PL = 

And in right angled PMC, 

PM = PM

Let AC =  then

 = AP + PC = ……….(i)

Now 

 

  

 

   ……….(ii)

And 

 

  [ and  is +ve as  )

 is minimum when 

 = 

 

Also 

= 

 

Putting these values in eq. (i),

Minimum length of hypotenuse = 

=  = 

i

More Material