Question

Triangle ABC has vertices at (-3, -1), (-1, 2) and (6, 1). What is the perimeter of triangle ABC, rounded to the nearest tenth?

Answer 1

Explanation:

Perimeter = 19.9unitsPerimeter

.............................

Answer 2

`Perimeter=19.9units`

Why?

We can find the perimeter of any triangle adding the length of its sides. Since we are given 3 points, we need to calculate the length of the three sides of the triangle, and then add them to know the perimeter of the triangle.

Let be the points:

A(-3,-1)

B(-1,2)

C(6,1)

- Distances

From A to B:

`d(A,B)=\sqrt{(-1-(-3))^(2)+(2-(-1)^(2)}\\\\d(A,B)=\sqrt{(2)^(2)+(3)^(2)}=√(4+9)=3.61units`

From A to C:

`d(A,C)=\sqrt{6-(-3))^(2)+(1-(-1)^(2)}\\\\d(A,B)=\sqrt{(9)^(2)+(2)^(2)}=√(81+4)=9.22units`

From B to C:

`d(B,C)=\sqrt{6-(-1))^(2)+(1-2)^(2)}\\\\d(A,B)=\sqrt{(7)^(2)+(-1)^(2)}=√(49+1)=7.07units`

Now, calculating the perimeter, we have:

`Perimeter=d(A,B)+d(A,C)+d(B,C)=3.61units+9.22units+7.07units\\\\Perimeter=19.9units`

Have a nice day!