Find the length of the side and perimeter of an equilateral triangle whose height is √3 cm.


Let BD be height of the triangle.
Since ABC is equilateral, BD is a perpendicular bisector.
AD = a/2
BD = √3 [given height = √3]
AB = a
Applying Pythagoras theorem in ABD
AB2 = AD2+BD2
a= (a/2)2+(√3)2
a= (a2/4)+3
(3/4)a2 = 3
a2 = 4
a = 2
Hence length of side of equilateral triangle is 2 cm.
Perimeter = 3×2 = 6 [Perimeter of equilateral triangle = 3×side]
Hence perimeter of equilateral triangle is 6 cm.

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