what is the measure of the altitude of an equilateral triangle whose side measures 6?

if you have an equilateral triangle with sides each measuring 6, then you can split it from the top down into two right triangles with a hypotenuse of 6 and a base of 3. Then, c sq. minus a sq. = b sq. Then find the square root of b sq. and you have the altitude of the triangle. In this example it's 5.196.

First, we need to know that a perpendicular line from the apex of an equilateral triangle to the opposite side bisects the side. (Draw a sketch - it will help). Therefore, the altitude is one side of a right triangle whose hypotenuse is 6, and whose other side is 3 (the opposite side of the triangle was divided in two, and 6/2 =3). Now from the quadratic equation we have, using a as the unknown altitude,

a^2 + 3^2 = 6^2, or a^2 +9 = 36 ----> a^2 = 27, a = sqrt(27)...you do it from here

a/x+1=c/x.......Rule is to get x to stand alone, so first we multiply both sides by x

x(a/x)+x(1)=x(c/x) cancelling x's where applicable we get

a+x=c------->x=c-a