What is the perimeter of a triangle?

Each schoolboy in the primary classes tried to find out what a triangle is and what is the perimeter of a triangle. Let's try to refresh it in memory.

The perimeter of a triangle is often the sum of the lengthsall parties. The general formula for finding the perimeter is: P = a + b + c. Here we simply add all the known sizes of the parties. But there are cases that either simplify or, on the contrary, complicate the task.

For an equilateral or regular triangle, the formula is P = 3a, and for an isosceles formula, P = 2a + b.

If the length of one side a and the values ​​of the adjacent angles α and β are known, then the perimeter can be found from the given perimeter formula P = a + sinα ∙ a / (sin (180 ° -α-β)) + sin ∙ a / (sinβ (180 ° -α-β)).

When it is known that the triangle is equilateral and the radii of the inscribed (r), as well as the circumscribed (R) circles, P = 6r√3 = 3R√3.