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Let a point P lies inside an equilater...

Let a point P lies inside an equilateral `triangle ABC` such that its perpendicular distances from sides are `P_(1),P_(2),P_(3)`.If side length of `triangle ABC` is 2 unit then

A

`(P_(1)+P_(2)+P_(3))` is equal to `sqrt(3)`

B

`(P_(1)+P_(2)+P_(3))` is equal to `4sqrt(3)`

C

Area of `triangle=sqrt(3)` Sq unit

D

Area of `triangle ABC =3` Sq unit

Text Solution

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The correct Answer is:
A, C
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Knowledge Check

  • Let AX_|_BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of DeltaABC from any point inside the triangle is :

    A
    Equal to BC
    B
    Equal to AX
    C
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    D
    Greater than AX

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

    A
    `asqrt3`
    B
    `asqrt2`
    C
    `2asqrt3`
    D
    None

  • The length of the perpendicular drawn from any point in the interior of an equilateral triangle to the respective sides are p_(1), p_(2) and p_(3) . The length of each side of the triangle is

    A
    (a) `(2)/(sqrt(3))(p_(1) + p_(2) + p_(3))`
    B
    (b) `(1)/(3)(p_(1) + p_(2) + p_(3))`
    C
    (c) `(1)/(sqrt(3))(p_(1) + p_(2) + p_(3))`
    D
    (d) `(4)/(sqrt(3))(p_(1) + p_(2) + p_(3))`

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