Question

ABC is an equilateral triangle with side of length a. Find the length of its altitude AD

Answer 1

Answer:

$\frac{ \sqrt{3} }{2} a$

Step-by-step explanation:

we have side of equilateral triangle as a .

i.e. AB=BC=AC=a

Also altitude of triangle is AD

So, By Pythagoras theorem in triangle ADC

${ac}^{2} = {ad}^{2} + {dc}^{2}$

i.e.

${a}^{2} = {ad}^{2} + ( \frac{a}{2}) {}^{2}$

so,

$ad {}^{2} = {a}^{2} - \frac{a {}^{2} }{4}$

so,

${ad}^{2} = \frac{ {3a}^{2} }{4}$

so,

$ad = \frac{ \sqrt{3} }{2} a$

therefore AD =a√3/2

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