Maths-
General
Easy
Question
If the length of the median of an equilateral triangle is x cm, then what is the area of triangle.
Hint:
In an equilateral triangle, median is the perpendicular of the base too.
The correct answer is: Equilateral triangle
It is given that length of the median = x cm
Let side of the triangle = a
![](data:image/png;base64,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)
Since median divides the base ⇒ BD =
Using Pythagoras in triangle ABD
AB2 = AD2 + BD2
a2 = x2 + (
)2
= x2 ⇒
= x
a = ![fraction numerator 2 x over denominator square root of 3 end fraction](data:image/png;base64,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)
Area of equilateral triangle = ![fraction numerator square root of 3 over denominator 4 end fraction a squared equals fraction numerator square root of 3 over denominator 4 end fraction open parentheses fraction numerator 2 x over denominator square root of 3 end fraction close parentheses squared](data:image/png;base64,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)
= ![fraction numerator square root of 3 over denominator 4 end fraction cross times fraction numerator 4 x squared over denominator 3 end fraction](data:image/png;base64,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)
= ![fraction numerator x squared over denominator square root of 3 end fraction](data:image/png;base64,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)
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