Home
Class 12
MATHS
A point on the hypotenuse of a triangle ...

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))`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT TAMIL|Exercise EXERCISE 6.5|48 Videos

  • APPLICATION OF INTEGRALS

    NCERT TAMIL|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

In a right angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?

Altitude on the hypotenuse of a right angle triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

The hypotenuse of a right angled triangle is 25cm an dits perimeter 56 cm. Find the length of the smallest side.

Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a,b,c are sides of a triangle and a^(2) + b^(2) = c^(2) , name the type of triangle.

The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle ?

NCERT TAMIL-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. Show that the normal at any point θ to the curve x = a costheta + a th...

    Text Solution

    |

  2. Find the intervals in which the function f given by f(x) = (4sin x-2...

    Text Solution

    |

  3. Find the intervals in which the function f given by f(x) =x^(3) +(1)/(...

    Text Solution

    |

  4. The area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1...

    Text Solution

    |

  5. A tank with rectangular base and rectangular sides, open at the top is...

    Text Solution

    |

  6. The sum of the perimeter of a circle and square is k, where k is some ...

    Text Solution

    |

  7. A window is in the form of a rectangle surmounted by a semicircular op...

    Text Solution

    |

  8. A point on the hypotenuse of a triangle is at distance a and b from th...

    Text Solution

    |

  9. Find the points at which the function f given by f (x) = (x-2)^(4)(x+1...

    Text Solution

    |

  10. Find the absolute maximum and minimum values of the function f given b...

    Text Solution

    |

  11. Show that the altitude of the right circular cone of maximum volume th...

    Text Solution

    |

  12. Let f be a function defined on [a, b] such that f ′(x) gt 0, for all x...

    Text Solution

    |

  13. Show that the height of the cylinder of maximum volume that can be ins...

    Text Solution

    |

  14. Show that height of the cylinder of greatest volume which can be inscr...

    Text Solution

    |

  15. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

    Text Solution

    |

  16. The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at th...

    Text Solution

    |

  17. The line y = mx + 1 is a tangent to the curve y^(2)= 4x if the value o...

    Text Solution

    |

  18. The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

    Text Solution

    |

  19. Find the equation of the normal to the curve x^(2) = 4y which passes t...

    Text Solution

    |

  20. The points on the curve 9y^(2) = x^(3) , where the normal to the curve...

    Text Solution

    |