The altitude of an equilateral triangle is 5 cm. Find the length of a side
Let "a" be the side of an equilateral triangle.
altitude will fall on the midpoint of opp. side
Hence This makes a right triangle with "a/2" as base "a" as hypotnuse
and altitude as height
So using Pythagoras Theorem
$\displaystyle a^2 = a^2/4 + (altitude)^2 $
Thus
$\displaystyle 3a^2/4 = (Altitude)^2 $
Hence
$\displaystyle Altitude = \pm \sqrt{\frac{3a}{4}} $
-ve value for length is inappropriate So the answer is tell me incase you can't digest this cake