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Question
If the area of an equilateral triangle is `16sqrt(3)` cm2, then the perimeter of the triangle is ______.
Options
48 cm
24 cm
12 cm
36 cm
Solution
If the area of an equilateral triangle is `16sqrt(3)` cm2, then the perimeter of the triangle is 24 cm.
Explanation:
Given, area of an equilateral triangle = `16sqrt(3)` cm2
Area of an equilateral triangle = `sqrt(3)/4` (side)2
`sqrt(3)/4`(Side)2 = `16sqrt(3)`
⇒ (Side)2 = 64
⇒ Side = 8 cm ...[Taking positive square root because side is always positive]
Perimeter of an equilateral triangle = 3 × Side
= 3 × 8
= 24 cm
Hence, the perimeter of an equilateral triangle is 24 cm.
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