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In equilateral triangle ABC with interio...

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of ` A B Cdot`

Text Solution

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Let the side equilateral triangleABC be a
Area of triangle, `Delta = (a xx 4 + a xx 5 + a xx 6)/(2)`
or `(a (4 + 5 + 6))/(2) = (sqrt3)/(4) a^(2)`
or `(15)/(2) = (sqrt3a)/(4)`
or `a = (30)/(sqrt3) = 10 sqrt3`
or `Delta = (sqrt3)/(4) xx 100 xx 3`
`= 75 sqrt3`
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