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ABC is an equilateral triangle whose cen...

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

D

Area of triangle is numerically half of the perimeter

Text Solution

Verified by Experts

The correct Answer is:
A
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)`
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