Question

triangle abc is an equilateral triangle with each side of length 2p if ad perpendicular bc then the value of ad is
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Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\triangle\;ABC\;is\;an\;equilateral\;triangle\;each\;side\;of\;length\;2p}$

$\mathsf{and\;AD\;\perp\;BC}$

$\underline{\textbf{To find:}}$

$\textsf{The value of AD}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\mathsf{Height\;of\;equilateral\;tirangle\;having\;side\;a\;is\;\dfrac{\sqrt{3}}{2}\,a}$

$\mathsf{=\dfrac{\sqrt{3}}{2}\,(2p)}$

$\mathsf{=\sqrt{3}\,p}$

$\implies\boxed{\mathsf{AD=\sqrt{3}\,p}}$

Answer 2

Height of Equilateral Triangle = (√3/2) a

$\sf \: \: = \frac{ \sqrt{3} }{2} \times (2p)$

$\sf = \sqrt{3} p$