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

Options

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
D. Area of triangle is numerically half of the perimeter

Answer

A

Explanation

Let h be the length of the altitude from A,
Distance from centroid to `BC = (h)/(3) = (122)/(sqrt(11^(2)+60^(2))) = (122)/(61) =2`
`:. h = 6` is height of `DeltaABC`
`:.` Area is `Delta = (h^(2))/(sqrt(3)) = 12 sqrt(3)`
Primeter, `P = 3 xx (2h)/(sqrt(3)) = 12 sqrt(3)`