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Question
The area of an equilateral triangle is `144sqrt3` cm2; find its perimeter.
Solution
Let each side of an equilateral triangle = x cm
∴ Its area = `sqrt(3)/4 ("side")^2`
= `sqrt(3)/4 x^2 = 144sqrt(3)` (given)
⇒ `x^2 = 144sqrt(3) xx 4/sqrt(3)`
⇒ `x^2 = 144 xx 4 ⇒ x^2 = 576`
⇒ x = `sqrt(576)` = 24 cm.
⇒ Each side = 24 cm
Hence perimeter = 3(24) = 72 cm.
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