Home
Class 12
MATHS
If the sum of the lengths of the hypoten...

If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is `pi/3dot`

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(5pi)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-B( Objective Type Questions ( One option is correct ))|31 Videos
  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option are correct ))|1 Videos
  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise TRY YOURSELF|39 Videos
  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is pi/3dot

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is pi/3dot

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is pi/3 .

If the sides of a right angled triangle are in A.P then the sines of the acute angles are

In the right triangle BAC, angle A=pi/2 and a+b=8 . The area of the triangle is maximum when angle C , is

If the difference between the two sides of a right-angled triangle is 2 cm and the area of the triangle is 24 cm^(2) , find the perimeter of the triangle.

If the lengths of the sides of a triangle are 3, 5, 7 , then its largest angle of the triangle is

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

AAKASH INSTITUTE ENGLISH-APPLICATION OF DERIVATIVES-Assignment SECTION-A (Competition Level Questions)
  1. If a variable tangent to the curve x^2y=c^3 makes intercepts a , bonx-...

    Text Solution

    |

  2. Difference between the greatest and the least values of the function f...

    Text Solution

    |

  3. If the sum of the lengths of the hypotenuse and another side of a righ...

    Text Solution

    |

  4. Let C be the curve y=x^3 (where x takes all real values). The tangent ...

    Text Solution

    |

  5. The interval on which f(x)=2x^(3)+9x^(2)+12x-1 is decreasing in

    Text Solution

    |

  6. The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) ...

    Text Solution

    |

  7. Divide 64 into two parts such that the sum of the cubes of two parts...

    Text Solution

    |

  8. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q ...

    Text Solution

    |

  9. A point on the parabola y^2=18 x at which the ordinate increases at tw...

    Text Solution

    |

  10. The real number x when added to its inverse given the minimum value of...

    Text Solution

    |

  11. Which of the following statement is true for the function f(x)={{:(sqr...

    Text Solution

    |

  12. The function f(x)=x^(3)-3x is

    Text Solution

    |

  13. If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive int...

    Text Solution

    |

  14. A curve is represented by the equations x=sec^2ta n dy=cott , where t ...

    Text Solution

    |

  15. Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x...

    Text Solution

    |

  16. Maximum area of a reactangle which can be inscribed in a circle of a...

    Text Solution

    |

  17. If atmosphere pressure at a height of h units is given by the function...

    Text Solution

    |

  18. The radius of cylinder of maximum volumne which can be inscribed in a...

    Text Solution

    |

  19. Let f(x)={{:(-|x-2|, ,x le 3 ),(x^(2)-2x-4,, x gt 3 ):} Then the n...

    Text Solution

    |

  20. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

    Text Solution

    |