Home
Class 11
MATHS
If A is the area and 2s is the sum of th...

If `A` is the area and `2s` is the sum of the sides of a triangle, then `Alt=(s^2)/4` (b) `Alt=(s^2)/(3sqrt(3))` `2RsinAsinBsinC` (d) `non eoft h e s e`

Text Solution

Verified by Experts

`25=a+b+c`
`A^2=s(s-a)(s-b)(s-c)`
`AM>=GM`
`(s+(s-a)+(s-b)+(s-c))/4=(s(s-a)(s-b)(s-c))^(1/4)`
`(4s-2s)/4=(A^2)^(1/4)`
`s/2>=(A)^(1/2)`
`AM>=GM`
`((s-a)+(s-b)+(s-c))/3>=((s-a)(s-b)(s-c))^(1/3)`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Given b=2,c=sqrt(3),/_A=30^0 , then inradius of A B C is (sqrt(3)-1)/2 (b) (sqrt(3)+1)/2 (c) (sqrt(3)-1)/4 (d) non eoft h e s e

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)< a < sqrt(3) (d) non eoft h e s e

The maximum area of the rectangle whose sides pass through the vertices of a given rectangle of sides a and b is (a) 2(a b) (b) 1/2(a+b)^2 (c) 1/2(a^2+b^2) (d) non eoft h e s e

If a,b,c are the sides of a triangle and s=(a+b+c)/2 , prove that 8(s-a)(s-b)(s-c)leabc .

If in a triangle (s-a)/11=(s-b)/12=(s-c)/13, then tan^2(A/2)

The area of the loop of the curve a y^2=x^2(a-x) is 4a^2s qdotu n i t s (b) (8a^2)/(15)s qdotu n i t s (16 a^2)/9s qdotu n i t s (d) None of these

If a , ba n dc 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 both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi] are real, then the values of b are [-2,0] (b) (-2,0) [-2,0] (d) non eoft h e s e

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

If alt=3cosx+5sin(x-pi/6)lt=b for all x then (a , b) is (a) (-sqrt(19),sqrt(19)) (b) (-17 ,17) (-sqrt(21),sqrt(21)) (b) non eoft h e s e

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the general values of x and y satisfying the equations 5sinx cosy...

    Text Solution

    |

  2. If (x^2)/4+(y^2)/9=1, then find the range of 2x+ydot

    Text Solution

    |

  3. If A is the area and 2s is the sum of the sides of a triangle, then Al...

    Text Solution

    |

  4. Find the general solution of : sqrt(3)sec2theta=2

    Text Solution

    |

  5. Find the value of 2cos^3(pi/7)-cos^2(pi/7)-cos(pi/7)

    Text Solution

    |

  6. In acute angled triangle A B C ,A D is the altitude. Circle drawn with...

    Text Solution

    |

  7. Show that sin^2 5^0+sin^2 10^0+sin^2 15^0+....+sin^2 90^0=9 1/2dot

    Text Solution

    |

  8. Solve (sin^3x/2-cos^3x/2)/(2+sinx)=(cosx)/3

    Text Solution

    |

  9. Prove that 4cos(2pi)/7dotcospi/7-1=2cos(2pi)/7dot

    Text Solution

    |

  10. Suppose alpha,beta,gammaa n ddelta are the interior angles of regular ...

    Text Solution

    |

  11. Find the value of cos^2pi/(16)+cos^2(3pi)/(16)+cos^2(5pi)/(16)+cos^2(7...

    Text Solution

    |

  12. Solve (sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(5)))/(cosx)=8,x in (0,pi/2)

    Text Solution

    |

  13. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15...

    Text Solution

    |

  14. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  15. If sin(120° – α) = sin(120° – β) and 0 < α, β < π then find the relati...

    Text Solution

    |

  16. Solve cosxcos2xcos3x=1/4

    Text Solution

    |

  17. Prove that sin 6^@ sin 42^@sin 66^@sin 78^@=1/16

    Text Solution

    |

  18. If the since of the angles A and B of a triangle ABCsatisfy the equati...

    Text Solution

    |

  19. Find the sign of the values of tan113^0-cos107^0=a and tan107^0-cos105...

    Text Solution

    |

  20. Solve the equation (sqrt(3))/2sinx-cosx=cos^2x

    Text Solution

    |