Question

Triangle ABC is an equilateral triangle with each side of length 2p if AD perpendicular to BC then what is the value of AD​

Answer 1

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

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

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

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

$\textsf{The value of AD}$

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

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

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

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

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

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

Answer 2

Step-by-step explanation:

H=

$\sqrt{3 \div 2 \times 2p } \\ = \sqrt{3p}$