Question

find the altitude of an equilateral triangle of side 10cm

Answer 1

Given,
Side = 10 cm

$height = \frac{ \sqrt{3} \times side }{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ \sqrt{3} \times 10 }{2} = 5 \sqrt{3}$ cm

Hence the altitude/height is 5√3 cm

Answer 2

Let the altitude be 'h'

Area of an equilateral triangle = √3/4×a²

where, a = side length

Also, Area of any Δ = 1/2×b×h

where, b = base length

            h = altitude

∴ √3/4×a² = 1/2×a×h ....................................(∵ b of an equilateral triangle = a

                                                                             as all the sides are equal )

or, √3/4×a = 1/2×h

∴ h = √3/4×a×2

       = (√3/2×10) cm = 5√3 cm