The length of a side of an equilateral triangle is 22 cm. what is the length of the altitude of the triangle?

So as you can see in the attached photo, I drew an equilateral triangle.

The first step was to write the measurements. In a equilateral triangle, the measurements are all the same. In this case 22 cm.

Next split the base in half. I did this with the green line. The base measurement is equal to 1/2 of 22 which is 11. This creates a 90° angle. (in red). Also in red I have marked the other angles. In an equilateral triangle all the interior angles are 60°. The top one is split in two.

Next, use the Pythagorean theorem. a² + b² = c².

In this problem C = 22 and b = 11.

a² + 11² = 22²

a² = 22² - 11²

a² = 484 - 121

a² = 363

a = √363

a = 19.05

The altitude of your triangle is 19.05 or √363 cm.

Hope that helps!

22

step-by-step explanation: