The height of an equilateral triangle having each side 12 cm, is

Foundation

Mathematics Foundation

Area of Triangle

area of triangle and properties

special points in triangle

Question

The height of an equilateral triangle having each side 12 cm, is

$6 \sqrt{6} cm$

$6 \sqrt{2} cm$

$6 \sqrt{3} cm$

$3 \sqrt{6} cm$

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The altitude of an equilateral triangle bisects the side on which it stands and forms right-angled triangles with the remaining sides.
So, CD = DB = 6 cm
Also in ΔADC, ∠ADC = 90°
Applying Pythagoras theorem gives

(AC)² = (CD)² + (AD)²

(12)² = (6)² + (AD)²

144 = 36 + (AD)²

(AD)² = 108

$AD = \sqrt{108} = 6 \sqrt{3} cm$

The height of equilateral triangle $= 6 \sqrt{3} cm$