What is the length of the altitude of an equilateral triangle whose perimeter is 15 inches?
1 Answer
Explanation:
First off, since the perimeter of the equilateral triangle (meaning that all 3 sides have the same length) is 15 inches, each side has a length of 5 inches.
Now we must recognize that an altitude of a triangle spans from one vertex to the opposite side, creating a right angle at the point of intersection. Thus, drawing the altitude inside of the equilateral triangle will create two 30-60-90 right triangles with a hypotenuse of 5 inches.
These angles make sense because equilateral triangles have 3 60 degree angles and the remaining angle (we already have one right angle - 90 degrees - and a 60 degree angle) must be 30 degrees since the angles in any triangle must sum to 180 degrees. Now there are many ways to find the length of the altitude, and I will present the easiest way in my opinion.
We will be using the fact that a 30-60-90 right triangle has side lengths in the respective ratio of 1-