Home
Class 10
MATHS
ABC is a Deltaand PQ is a line intersect...

ABC is a Deltaand PQ is a line intersecting AB at P and AC at Q. If `AP= 1cm, PB = 3cm, AQ= 1.5 cm" and "QC= 4.5`, prove that ar(ABC)= 16 ar(APQ).

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    KUMAR PRAKASHAN|Exercise PRACTICE THOROUGHLY|20 Videos

  • TRIANGLES

    KUMAR PRAKASHAN|Exercise OBJECTIVE QUESTIONS|37 Videos

  • TRIANGLES

    KUMAR PRAKASHAN|Exercise EXERCISE 6.6|15 Videos

  • SURFACE AREAS AND VOLUMES

    KUMAR PRAKASHAN|Exercise TEST YOUR SKILLS|5 Videos

Similar Questions

Explore conceptually related problems

ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, BP = 3cm, AQ = 1.5 cm and CQ = 4.5 cm, prove that area of Delta APQ = (1)/(16) ( area of Delta ABC ).

Fill in the blanks so as to make each of the following statements true : In DeltaABC , points P and Q lie on sides AB and AC respectively such that PQ||BC . If AP= 5cm, PB= 12 cm and AQ= 8 cm, then AC="………"cm .

In Delta ABC , M and N are the midpoints of AB and AC respectively. If AB = 8 cm, AC = 7 cm and MN = 4.5 cm, find the perimeter of Delta ABC .

In the given figure CB||QR" and "CA||PR . If AQ= 12 cm, AR= 20 cm and PB= CQ= 15 cm, find PC and BR.

In Delta ABC , P, Q and R are the midpoints of AB, BC and CA respectively. If PQ = 5 cm, QR = 8 cm and RP = 6.5 cm, find the perimeter of Delta ABC .

In triangleABC , medians AC, BE and CF intersect at point G. Prove that ar(GAB)=ar(GBC)=ar(GCA)= 1/3 ar(ABC).

In the given figure, DeltaABR ~ DeltaPQR . If PQ= 30 cm, AB= 45 cm, AP= 72 cm and QR= 42 cm, find PR, AR and BR.

In quadrilateral ABCD, AB = 9 cm, BC = 12 cm, CD = 8.5 cm, DA = 8.5 cm and AC = 15 cm. Find the area of quadrilateral ABCD.

Fill in the blanks so as to make each of the following statements true : In DeltaABC , AD is the bisector of /_A and D lies on BC. If AB= 6 cm, AC= 5 cm and BD= 3 cm, then BC="……….."cm .

In triangleABC , P,Q and R are the midpoints of AB, BC and CA respectively. If ar(ABC)=32 cm^2 , then ar(PQR)= ____ cm^2

KUMAR PRAKASHAN-TRIANGLES-TEST YOUR SKILLS
  1. In the given figure, if (EA)/(EC)=(EB)/(ED) prove that DeltaEAB ~ De...

    Text Solution

    |

  2. In the given figure, if (EA)/(EC)=(EB)/(ED) prove that AB||CD

    Text Solution

    |

  3. In the given figure, ABC and DBC are two triangles on the same base BC...

    Text Solution

    |

  4. In the given figure, DeltaABC is a right angled Deltawith /B= 90^(@) a...

    Text Solution

    |

  5. The areas of two similar triangles are 100 cm^(2)" and "49 cm^(2) resp...

    Text Solution

    |

  6. The areas of two similar triangles are 169 cm^(2)" and "121 cm^(2) res...

    Text Solution

    |

  7. ABC is a Deltaand PQ is a line intersecting AB at P and AC at Q. If AP...

    Text Solution

    |

  8. In DeltaPQR, /Q= 90^(@). Equilateral triangles APQ, BQR and CPR are de...

    Text Solution

    |

  9. Two isosceles triangles have equal vertical angles and their areas are...

    Text Solution

    |

  10. In DeltaABC, AD bot BC, point D lies on BC. If AC^(2)=CD*BD, prove tha...

    Text Solution

    |

  11. In the figure, AC is the length of a pole standing vertical on the gro...

    Text Solution

    |

  12. In DeltaABC, /A= 90^(@)" and "AD bot BC. Prove that (1)/(AD^2)=(1)/(AB...

    Text Solution

    |

  13. In an equilateral triangle with side a, prove that, the altitude is ...

    Text Solution

    |

  14. In an equilateral triangle with side a, prove that, the area of the ...

    Text Solution

    |

  15. BL and CM are medians of a DeltaABC right angled at A. Prove that 4(BL...

    Text Solution

    |

  16. ABC is a Deltain which /B gt 90^(@)" and "AD bot CB produced. Prove th...

    Text Solution

    |

  17. ABC is a Deltain which /B lt 90^(@)" and "AD bot CB. Prove that AC^(2...

    Text Solution

    |

  18. A ladder 15 m long reaches a window which is 9 m above the ground on o...

    Text Solution

    |

  19. Find the length of the longest stick that can be placed in a cuboidal ...

    Text Solution

    |

  20. The given figure shows the distances covered by Ariv from place a to p...

    Text Solution

    |