Home
Class 9
MATHS
Parallelogram A B C D and rectangle A B ...

Parallelogram `A B C D` and rectangle `A B E F` have the same base `A B` and also have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle. GIVEN : `A ||^(gm)A B C D` and a rectangle `A B E F` with the same base `A B` and equal areas. TO PROVE : Perimeter of `||^(gm)A B C D` > Perimeter of rectangle ABEF i.e. `A B+B C+C D+A D > A B+B E+E F+A F`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|247 Videos

  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Prove that the perimeter of a triangle is greater than the sum of the three medians. GIVEN : A A B C in which A D ,B E and C F are its medians. TO PROVE : A B+B C+A C > A D+B E+C F

If A B C D is a rectangle with /_B A C=32^0, find the measure of /_D B C

In a rectangle A B C D , prove that A C B~= C A Ddot

If A B C D is a rectangle with /_B A C=32^0, find the measure of /_D B C .

A B C D is a rectangle with /_A B D=40^0dot Determine /_D B C

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( /_\A D F)=a r( /_\D C E).

In Figure, A B C D is a quadrilateral and B E || A C and also B E meets D C produced at E . Show that area of triangle A D E is equal to the area of the quadrilateral A B C D .

Rectangle ABCD has area 200.An ellipse with area 200pi passes through A and C and has foci at B and D. Find the perimeter of the rectangle.

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. A B C D is a parallelogram and O is any point in its interior. Prove t...

    Text Solution

    |

  2. A quadrilateral A B C D is such that diagonal B D divides its area in ...

    Text Solution

    |

  3. Parallelogram A B C D and rectangle A B E F have the same base A B and...

    Text Solution

    |

  4. O is any point on the diagonal B D of the parallelogram A B C D. Prove...

    Text Solution

    |

  5. Triangles A B C and DBC are on the same base B C with A, D on opposite...

    Text Solution

    |

  6. D and E are points on sides AB and AC respectively of DeltaA B Csuch...

    Text Solution

    |

  7. If the medians of a triangle A B C intersect at G , show that a r( tr...

    Text Solution

    |

  8. D, E and F are respectively the mid-points of the sides BC, CA and AB...

    Text Solution

    |

  9. B D is one of the diagonals of a quadrilateral A B C D. A M and C N ...

    Text Solution

    |

  10. A B C D is a quadrilateral. A line through D , parallel to A C , mee...

    Text Solution

    |

  11. If the median of a △ABC intersect at G. show that ar (△AGC) = ar (△AGB...

    Text Solution

    |

  12. X Y is a line parallel to side B C of triangle A B C . If B E II AC a...

    Text Solution

    |

  13. E , F , G , H are respectively, the mid-points of the sides A B ,B C ...

    Text Solution

    |

  14. X Y is a line parallel to side B C of /\ A B C. B E || AC and C F || A...

    Text Solution

    |

  15. E , F , G , H are respectively, the mid-points of the sides A B ,B C ,...

    Text Solution

    |

  16. The side A B of a parallelogram A B C D is produced to any point Pdot ...

    Text Solution

    |

  17. Any point D is taken in the base B C of a triangle A B C\ a n d\ A...

    Text Solution

    |

  18. In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...

    Text Solution

    |

  19. In a parallelogram A B C D ,E ,F are any two points on the sides A B a...

    Text Solution

    |

  20. In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is prod...

    Text Solution

    |