From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is
Explanation:
The figure can be drawn as below.
Sum of areas of three smaller ∆s = Area of ∆ABC
⇒ 12×h1×a + 12×h2×a + 12×h3×a = 34a2
⇒ 12×s×a = 34a2
⇒ a = 2s3
∴ Area of ∆ABC = 34a2 = 34×43×s2 = s23
Hence, option (a).
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