Question
From a point in he interior of an equilateral triangle , the perpendicular distance of the side are `sqrt(3`) cm . The perimeter (in cm) of the triangle is :
Answer: Option C
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Let each of the triangle be a cm.
Then , ar (`Dela` AOB) + ar (`Delta` AOC) = ar (`Delta` ABC)
`rArr 1/2 xx a xx sqrt(3) + 1/2 xx a xx 2sqrt(3) + 1/2 xx a xx 5sqrt(3)` = `sqrt(3)/4 a^2`
`rArr a/2 sqrt(3) (1 + 2 + 3) = sqrt(3)/4 a^2`
`rArr a = 16`
`:.` Perimeter = (3 x 16) = 48 cm.
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