Question

The perimeter of an equilateral triangle is 26 centimeters. Find the altitude of the triangle

Answer 1

We have P = 3 x a (the formula of the perimeter); 26 = 3 x a ; we obtain a = 26/3;

Then, we have  the Pythagorean Theorem in one of two rectangular and congruent triangles :

h² = a² - (a/2)² = a² - a²/4 = 4a²/4 - a²/4 = 3a²/4

It follows that

h = √(3a²/4) = a√3/2 ≈ 0,866*a ≈ 7,5 centimeter.