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Question
The perimeter of an equilateral triangle is 60 m. The area is ______.
Options
`10sqrt(3)` m2
`15sqrt(3)` m2
`20sqrt(3)` m2
`100sqrt(3)` m2
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Solution
The perimeter of an equilateral triangle is 60 m. The area is `underlinebb(100sqrt(3) m^2)`.
Explanation:
Let each side of an equilateral be x.
Then, perimeter of an equilateral triangle = 60 m
x + x + x = 60
⇒ 3x = 60
⇒ x = `60/3` = 20 m
Area of an equilateral triangle = `sqrt(3)/4` (Side)2
= `(sqrt(3)/4) xx 20 xx 20`
= `100sqrt(3)` m2
Thus, the area of triangle is `100sqrt(3)` m2.
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