how do i find the height of a triangle with a measurment of 20mm on all sides?

An equilateral triangle with 20 mm on both sides can be turned into two similar right triangles by taking the top of the triangle and dropping a line down so it is perpendicular to the base. The base is now cut in half to be 10 mm each. The hypotenuse is known as 20 mm, and the "height" you are asked about is your unknown leg. So you can now solve this using Pythagorean Theorem:

a² + b² = c²

10² + b² = 20²

100 + b² = 400

b² = 300

b = √300

b = √(100 * 3)

b = 10√3 mm