Find the height of an equilateral triangle of side 12cm.
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$\triangle\text{ABC}$ is an equilateral triangle in which all side are equal. Therefore, AB = BC = AC = 12cm If BC = 12cm Then, BD = BC = 6cm
In $\triangle\text{ADB},$ $\text{AB}^2=\text{AD}^2+\text{BD}^2$ (By applying pythagoras theorem) $\text{AD}^2=\text{AB}^2-\text{BD}^2$ $\text{AD}^2=\Big[(12)^2-(6)^2\Big]\text{cm}^2$ $\text{AD}^2=\sqrt{108}\text{cm}$ $\text{AD}=\sqrt{108}\text{cm}=6\sqrt{3}\text{cm}$ Hence the height of the triangle is $6\sqrt{3}\text{cm}$
In $\triangle\text{ADB},$ $\text{AB}^2=\text{AD}^2+\text{BD}^2$ (By applying pythagoras theorem) $\text{AD}^2=\text{AB}^2-\text{BD}^2$ $\text{AD}^2=\Big[(12)^2-(6)^2\Big]\text{cm}^2$ $\text{AD}^2=\sqrt{108}\text{cm}$ $\text{AD}=\sqrt{108}\text{cm}=6\sqrt{3}\text{cm}$ Hence the height of the triangle is $6\sqrt{3}\text{cm}$
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