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An equilateral triangle ABC has its cent...

An equilateral triangle ABC has its centroid at the origin and the base BC lies along the line `x + y = 1`. Area of the equilateral `DeltaABC` is

Text Solution

Verified by Experts

In the given figure,
`l=CD=1/sqrt2`
`AC=2l=2/sqrt2`
`AD=2l=2/sqrt2`
In `triangle ADC`
`cos30^@=(AD)/(AC)+sqrt3/2=(AD)/a`
`a=(2AD)/sqrt3=sqrt6`
`Area = sqrt3/4a^2=sqrt3/4*6=3sqrt3/2sq.unit`
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Knowledge Check

  • ABC is an equilateral triangle whose centroid is origin and base BC is along the line 11x +60y = 122 . Then

    A
    Area of the triangle is numerically equal to the perimeter
    B
    Area of triangle is numerically double the perimeter
    C
    Area of triangle is numerically three times the perimeter
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    D
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    (-1,-1)
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