Question

In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

• A. $\sqrt{4}5$
• B. $\sqrt{2}7$
• C. $\sqrt{3}0$
• D. $\sqrt{2}5$

Answer 1

The correct option is B $\sqrt{2}7$

We know that,
in an equilateral triangle the Median is also the Altitude.


Using Pythagoras theorem,
$6^2=(AD{)}^2+3^2$
$(AD{)}^2=6^2-3^2$
$(AD{)}^2=36-9$
AD = $\sqrt{2}7cm$