Question

Find the altitude of and equilateral triangle when each of its side is' a' cm

Answer 1

In triangle ABC
BD= AB/2
ie
BD= a/2-----(1)

Next,
In Triangle ABD , angle D = 90°
By Pythagoras Theorem,
${ab}^{2} + {bd}^{2} = {ad}^{2}$
ie

${a}^{2} + \frac{ {a}^{2} }{4} = {ad}^{2} - - - - by(1)$
ie

$\frac{ {5a}^{2} }{4} = {ad}^{2}$
Therefore

AD =
$\frac{ \sqrt{5}a }{2}$