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

So the height drops to the side of the triangle at a 90 degree angle. It follows that the height of the triangle divides it into 2 right-angled triangles with a base of 90 degrees.

Omitting the height, we get 2 equal right-angled triangles, where 1 leg is 14 cm, the second leg is half the hypotenuse.

Take the hypotenuse for x, then 1 leg is 14 cm, the second – 0.5 * x.

Pythagorean theorem
Let’s recall the Pythagorean theorem:

The sum of the squares of the legs is equal to the square of the hypotenuse of a right-angled triangle.

a ^ 2 + b ^ 2 = c ^ 2.

Based on the formula, we will compose the equation:

14 ^ 2 + (0.5 * x) ^ 2 = x ^ 2;

Let’s solve the resulting equation:

14 ^ 2 + (0.5 * x) ^ 2 = x ^ 2;
196 + 0.25 * x ^ 2 = x ^ 2;
x ^ 2 – 0.25 * x ^ 2 = 196;
0.75 * x ^ 2 = 196;
x ^ 2 = 196 / 0.75 = $ 261
x = √261 = 16.2;
So, the side of the triangle is about 16.2 cm.

Answer: 16.2 cm.