Classify each triangle by its sides. Then find the perimeter.

Question

A(4,1)

B(-3,6)

C(0,0)

 

and

 

E(-1.6)

F(1,-3)

D(5,0)

Answer 1

A(4,1), B(–3,6), C(0,0) are vertices of ΔABC.

 

If you graph these points you get something like this:

 

B

*

 

 

 

 

                                      * A

              *C

 

That looks like a Scalene Triangle (no sides equal). Let's find the side lengths to prove it.

 

AB^2 = (4 – –3)^2 + (1 – 6)^2 = 49 + 25 = 74

AB = √(74)

 

BC^2 = (0 – –3)^2 + (0 – 6)^2 = 9 + 36 = 45

BC = √(45) = 3√(5)

 

AC^2 = (4 – 0)^2 + (1 – 0)^2 = 16 + 1 = 17

AC = √(17)

 

None of the sides are equal, so the triangle is Scalene.

 

The perimeter is AB + BC + AC = √(74) + 3√(5) + √(17)

 

Analyze ΔDEF the same way.