Question

in an equilateral triangle abc if ad is perpendicular to bc and BC = x cm find AD in terms of x

Answer 1

you may go through the above answer.
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Answer 2

The value of $AD$ is $\frac{\sqrt{3}x }{2} cm$

Step-by-step explanation:

Given,

An equilateral $\triangle ABC$ where $AD\perp BC$ and $BC=x\,cm$

From $\triangle ABD$ is a right angle triangle,

∴ $AB^{2} =BD^{2} +AD^{2}$

⇒$AD^{2}= AB^{2} -BD^{2}$

⇒$AD^{2} =x^{2} -(\frac{x}{2}) ^{2}$  (where $BD=\frac{1}{2}BC$)

⇒$AD^{2} =\frac{3x^{2} }{4}$

⇒$AD=\sqrt{\frac{3x^{2} }{4} }$

∴ $AD=\frac{\sqrt{3}x }{2} cm$

∴ The value of $AD$ is $\frac{\sqrt{3}x }{2} cm$