Home
Class 11
MATHS
A parallelogram containing a 60^0 angle ...

A parallelogram containing a `60^0` angle has perimeter `p` and its longer diagonal is of length `d` Find its area.

Text Solution

Verified by Experts

Perimeter=`2(x+y)=P`
`x+y=P/2-(1)`
`In/_ABD`
`d^2=y^2sin^2 60+(x+ycos60)^2`
`d^2=y^2sin^2 60+x^2+y^2cos^2 60+2xycos60`
`d^2=x^2+y^2+2xy*1/2`
`d^2=x^2+y^2+xy`
`d^2=(x+y)^2-xy`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

ABCD is a parallelogram and angleA = 60^(@) . Find the remaining angles.

The equations of two adjacent side of a parallelogram are 4x+5y=0 and 7x+2y=0 . If the equation of its one diagonal be 11x+7y=9 , find the equation of its other diagonal.

A polygon has 44 diagonals. The number of its sides is

Two sides of a parallelogram are along the lines x+y=3 and x=y+3. If its diagonals intersect at (2, 4) , then one of its vertices is

The length of diagonal of a cube is 4 sqrt3cm . Find its total surface area.

The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2hatj-3hatk . Find the unit vector parallel to its diagonal Also , find its area.

The area of equilateral triangle is 25 sq-cm Find its perimeter.

A(-3, 5) and B(1, 7) are two consecutive vertices of a parallelogram. If the point of intersection of its diagonals be (1, 1), then find its other two vertices.

A triangle with equal sides has perimeter 9 cm. Then find the area of the triangle

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If in a triangle (1-r1/r2)(1-r1/r3)=2,then the triangle is

    Text Solution

    |

  2. Let alpha and beta be the roots of the quadratic equation x^(2) sin th...

    Text Solution

    |

  3. A parallelogram containing a 60^0 angle has perimeter p and its longer...

    Text Solution

    |

  4. If r/(r1)=(r2)/(r3), then

    Text Solution

    |

  5. If sin(sinx+cosx)=cos(cosx-sinx), and largest possible value of sinx ...

    Text Solution

    |

  6. If 0lt=xlt=pi/3 then range of f(x)=sec(pi/6-x)+sec(pi/6+x) is

    Text Solution

    |

  7. For each natural number ngt=2, prove that sinx1cosx2+sinx2cosx3+...+si...

    Text Solution

    |

  8. The values of x1 between 0 and 2pi , satisfying the equation cos3x+c...

    Text Solution

    |

  9. If y=(sin^4x-cos^4x+sin^2xcos^2x)/(sin^4x+cos^4x+sin^2xcos^2x),x in (0...

    Text Solution

    |

  10. In an acute angled triangle A B C ,r+r1=r2+r3a n d/B >pi/3, then (a) b...

    Text Solution

    |

  11. If un=sin^("n")theta+cos^ntheta, then prove that (u5-u7)/(u3-u5)=(u3)/...

    Text Solution

    |

  12. If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x...

    Text Solution

    |

  13. The general solution of the equation sin^(100)x-cos^(100)x=1 is

    Text Solution

    |

  14. If in triangle A B C ,sumsin(A/2)=6/5a n dsumI I1=9 (where I1,I2 a n d...

    Text Solution

    |

  15. Prove that in A B C ,tanA+tanB+tanCgeq3sqrt(3,) where A , B , C are...

    Text Solution

    |

  16. In triangle A B C ,/A=60^0,/B=40^0,a n d/C=80^0dot If P is the center ...

    Text Solution

    |

  17. If cos3x+sin(2x-(7pi)/6)=-2 , then show that x is of the form π / 3(6...

    Text Solution

    |

  18. Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

    Text Solution

    |

  19. If H is the othrocenter of an acute angled triangle ABC whose circumci...

    Text Solution

    |

  20. The number of solutions of the equation 1+cosx+cos2x+sinx+sin2x+sin3x=...

    Text Solution

    |