If the length of a median of an equilateral triangle is Xcm find it's area??
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Median in equilateral triangle is perpendicular bisector of the side.
when side is a cm, then length of median will be
x = √[(a)²-(a/2)²]
=√(3a²/4)
=(a/2)√3
⇒x = (a/2)√3
⇒a = 2x/√3
now. area = (√3/4)a²
= (√3/4)×(2x/√3)²
= x²/√3 cm²
when side is a cm, then length of median will be
x = √[(a)²-(a/2)²]
=√(3a²/4)
=(a/2)√3
⇒x = (a/2)√3
⇒a = 2x/√3
now. area = (√3/4)a²
= (√3/4)×(2x/√3)²
= x²/√3 cm²
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