Find the perimeter of the triangle with vertices A(–5, –2), B(–2, –2), and C(–5, 2).

Answer 1

A triangle has three sides and three angles

The side lengths are the lengths of the line segments AB, BC, and CA. These may be found using the endpoints of the segments with the distance formula:

The distance from point P(x₁,y₁) to point Q(x₂,y₂) is:

Distance = √ ( (x₂ - x₁)² + (y₂ - y₁)² )

It is a good learning exercise to plug in all the numbers. Then, you will realize that some x-values or y-values are the same (you would also see this if you graphed the triangle).

AB = 3

BC = 5

CA = 4

Also, note that 3-4-5 are integer side lengths for a right triangle. The integer triples that satisfy the Pythagorean Theorem are called Pythagorean Triples. They appear in many, many homework problems and in standardized tests.

Perimeter= 3 + 5 + 4 = 12

Answer 2

To find the perimeter of the triangle, find the lengths of each side of the triangle using the distance formula.

Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter.

Distance formula:

Points A and B:

d = √(-2 +5)² + (-2 + 2)²

d = √ 3² + 0

d = √9

d = 3

Points B and C:

d = √ (-5 + 2)² + (2 +2)²

d = √ -3² + 4²

d = √ 25

d = 5

Points C and A:

d = √ (-5 + 5)² + (-2 -2)²

d = √ 0 + -4²

d = √ 16

d = 4

Perimeter= 3 + 5 + 4 = 12