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In an equilateral triangle of side 2a cm calculate the length of its altitude

Posted by Firoj Khan 6 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

Let {tex}\triangle{/tex}ABC be an equilateral triangle.
We know that in an equilateral triangle the altitude is same as the median.
So, BD=DC=a cm
By Pythagoras theorem,
AC²=AD²+DC²
{tex}\Rightarrow{/tex} AD²=AC²-DC²
{tex}\Rightarrow{/tex} AD²=(2a)² -a²
{tex}\Rightarrow{/tex} AD²= 4a² - a²
{tex}\Rightarrow{/tex} AD²=3a²
{tex}\Rightarrow{/tex} AD={tex}\sqrt 3 {/tex} a cm
So, length of the altitude is {tex}\sqrt 3 {/tex} a cm.

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