Question
Download Solution PDF'O' is a point in the interior of an equilateral triangle. The perpendicular distance from 'O' to the sides are \(\sqrt3\) cm, 2\(\sqrt3\) cm, 5\(\sqrt3\) cm. The perimeter of the triangle is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The perpendicular distance:
P1 = √3; P2 = 2√3; P3 = 5√3
Concept used:
Height of an equilateral triangle = (√3 × side)/2
Height of equilateral triangle = sum of perpendicular distance with point
Perimeter of an equilateral triangle = 3 × side
Calculation:
Height of equilateral triangle = sum of perpendicular distance
⇒ (√3 × side)/2 = P1 + P2 + P3
⇒ (√3 × side)/2 = √3 + 2√3 + 5√3
⇒ side = 8 × 2 = 16 cm
Perimeter of an equilateral triangle = 3 × side
⇒ 3 × 16 = 48 cm
∴ The correct answer is 48 cm.
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