'O' is a point in the interior of an equilateral triangle. The perpendicular distance from 'O' to the sides are $\sqrt{3}$cm, $2\sqrt{3}$cm, $5\sqrt{3}$cm. The perimeter of the triangle is:
Answer & explanation
Correct answer: option 1
We know that,
Height of an equilateral triangle = \(\frac{\sqrt {3}}{2}\)Side
Height of equilateral triangle = sum of perpendicular distance with point
Perimeter of an equilateral triangle = 3 × side
The perpendicular distance = P1 = \(\sqrt {3}\)
P2 = 2\(\sqrt {3}\)
P3 = 5\(\sqrt {3}\)
Height of equilateral triangle = (\(\sqrt {3}\) × side) × \(\frac{1}{2}\) = P1 + P2 + P3
= (\(\sqrt {3}\) × side) × \(\frac{1}{2}\) = \(\sqrt {3}\) + 2\(\sqrt {3}\) + 5\(\sqrt {3}\)
= side = 8 × 2 = 16 cm
Perimeter of an equilateral triangle = 3 × side = 3 × 16 = 48 cm