Calculate the perimeter of the triangle with the vertices A (2; 3) B (1; 4) C (-4; 2).
March 28, 2021 | education
| The perimeter of the triangle ABC is calculated by the formula:
P = AB + BC + AC.
It is necessary to find the lengths of the sides of the triangle, for this we first find the coordinates of the vectors AB, BC and AC:
AB (1 – 2; 4 – 3), AB (-1; 1)
BC (- 4 – 1; 2 – 4); BC (-5; -2)
AC (- 4 – 2; 2 – 3) AC (-6; -1)
The length of a vector by its coordinates is calculated by the formula:
L ^ 2 = x ^ 2 + y ^ 2.
Let’s find the lengths of the sides of the triangle:
AB ^ 2 = 1 + 1 = 2; AB = √2
BC ^ 2 = 25 + 4 = 29; BC = √29
AC ^ 2 = 36 + 1 = 37; AC = √37
We get the perimeter of the triangle:
P = √2 + √29 + √37, which is approximately equal to 12.9 units.
Answer: √2 + √29 + √37 or 12.9 units.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.