Question

In an equilateral triangle ABC, AD is the median from vertex A to the side BC, the length of median is $\sqrt{2}7$ cm, then find the length of the equilateral triangle.

Answer 1

We know that,
In an equilateral triangle the Median is also the Altitude.
Let the side of the triangle measure $xcm$
Using Pythagorean theorem

$(\sqrt{2}7{)}^2+(\frac{x}{2}{)}^2=x^2$
$x^2-(\frac{x}{2}{)}^2=(\sqrt{2}7{)}^2$
$\frac{3x^2}{4}=27$
$x^2=\frac{27\times 4}{3}$
$x^2=36$
$x=6cm$