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

User Knetic
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2 Answers

3 votes

Explanation:

Perimeter = 19.9unitsPerimeter

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

User Mbaros
by
8.7k points
6 votes


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!

User Champignac
by
8.1k points

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