What is the side of an equilateral triangle that is 14 cm high?

An equilateral (or regular) triangle is a triangle in which all sides and angles are equal (the degree measures of all angles are 60˚).
In such a triangle, the heights, bisectors and medians drawn from one vertex coincide and are found according to the same formula:
h = l = m = (a√3) / 2,
where a is the length of the side of the triangle.
Substitute the values specified in the condition into this formula:
(a√3) / 2 = 14.
Using the main property of the “cross to cross” proportion, we find the length of the side of the triangle:
a = (2 * 14) / √3 = 28 / √3 = (28√3) / 3 (cm).
Answer: a = (28√3) / 3 cm.