Home
Class 10
MATHS
ABC is an equilateral triangle of sid...

ABC is an equilateral triangle of side 2a. Find each of its altitudes.

A

`asqrt3`

B

`asqrt2`

C

`2asqrt3`

D

None

Text Solution

Verified by Experts

The correct Answer is:
A
As `Delta ABC` is an equilateral triangle, its altitude will also be the median.
If we draw a median `AD` to `BC`. Then,
`BD = DC and /_ADB=90^@`
We are given,
`AB = AC = BC = 2a`
So,`BD = DC = (BC)/2 = a`
As, `Delta ABD` is a right angle triangle,
`AB^2 = AD^2+BD^2`
...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NCERT ENGLISH|Exercise EXERCISE 6.3|16 Videos

  • TRIANGLES

    NCERT ENGLISH|Exercise Exercise 6.2|10 Videos

  • TRIANGLES

    NCERT ENGLISH|Exercise Exercise 6.1|3 Videos

  • SURFACE AREAS AND VOLUMES

    NCERT ENGLISH|Exercise Exercise 13.3|9 Videos

Similar Questions

Explore conceptually related problems

Construct an equilateral triangle of sides 6 cm each.

Find the coordinates of the vertices of an equilateral triangle of side 2a as shown in Figure.

Three particle of mass m each are placed at the three corners of an equilateral triangle of side a. Find the work which should be done on this system to increase the sides of the triangle to 2a.

Three particle of mass m each are placed at the three corners of an equilateral triangle of side a. Find the work which should be done on this system to increase the sides of the triangle to 2a.

Three particle of mass m each are placed at the three corners of an equilateral triangle of side a. Find the work which should be done on this system to increase the sides of the triangle to 2a.

Write the negatin of each of the statement : ABC is an equilateral triangle if and only if it is equiangular.

ABC is an equilateral triangle. Length of each side is 'a' and centroid is point O. Find vec(AB)+vec(BC)+vec(CA)

ABC is an equilateral triangle. Length of each side is 'a' and centroid is point O. Find If |vec(AB)+vec(BC)+vec(AC)|=na then n = ?

ABC is an equilateral triangle. Length of each side is 'a' and centroid is point O. Find If vec(AB)+vec(AC)=nvec(AO) then n = ?

ABC is an equilateral triangle of side 2m. If vec(E ) = 10 NC^(-1) then V_(A) - V_(B) is

NCERT ENGLISH-TRIANGLES-Exercise 6.5
  1. ABC is an isosceles triangle with AC = BC. If A B^2=2A C^2, prove tha...

    Text Solution

    |

  2. D and E are points on the sides CA and CB respectively of a triangle ...

    Text Solution

    |

  3. Tick the correct answer and justify: In DeltaA B C.AB = 6sqrt(3)cm. ...

    Text Solution

    |

  4. PQR is a triangle right-angled at P and M is a point on QR such that ...

    Text Solution

    |

  5. A guy attached wire to a vertical pole of height 18m is 24 m long an...

    Text Solution

    |

  6. In Figure, ABD is a triangle right-angled at A and A C|B D. Show tha...

    Text Solution

    |

  7. The perpendicular from A on side BC of a ABC intersects BC at D such t...

    Text Solution

    |

  8. ABC is an isosceles right triangle, right-angled at C . Prove that:...

    Text Solution

    |

  9. Two poles of heights 6 m and 11m stand on a plane ground. If the dist...

    Text Solution

    |

  10. A ladder 10m long reaches a window 8 m above the ground. Find the dis...

    Text Solution

    |

  11. In an equilateral triangle ABC, D is a point on side BC such that B D=...

    Text Solution

    |

  12. In figure, O is a point in the interior of a triangle ABC, O D|B C ,O...

    Text Solution

    |

  13. In an equilateral triangle, prove that three times the square of one ...

    Text Solution

    |

  14. An aeroplane leaves an airport and flies due north at a speed of 1000...

    Text Solution

    |

  15. Sides of triangles are given below. Determine which of them are right...

    Text Solution

    |

  16. ABC is an equilateral triangle of side 2a. Find each of its altitud...

    Text Solution

    |

  17. Prove that the sum of the squares of the sides of a rhombus is equal ...

    Text Solution

    |