Why did Matt get upset when his teacher called him average?
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All sides are equal in an equilateral triangle and the perpendicular bisects the side too.
so BC will be bisected and the segments be 5 each.
you can use Pythagoras theorem to find the altitude length, hypotenuse will be one side of the triangle.
$h^2=100-25=75$
$h=\sqrt{75}=5\sqrt3$