Question

Lliana wants to find the perimeter of triangle ABC. She uses the distance formula to determine the length of AB. Finish

lliana's calculations to find the length of AB.
Bi(3,6)
A(-1,3
c (3,3)
ABV(-1-3)2 + (3-6)
- V-4)2+(-3)?
What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.

Answer 1

The hypotenuse is 5, the sides are 3 and 4. The perimeter is the addition of those 3 numbers.

5+4+3 = 12 units

For future reference, if the sides of a right triangle are any multiples of 3 and 4, the hypotenuse is the same multiple of 5. This triangle has sides with lengths 3, 4, and 5, and a triangle with sides 9 and 12 would have a hypotenuse of 15 :)

Explanation:

Answer 2

12 units is the perimeter of triangle ABC.

Explanation:

Coordinates of triangle ABC:

A = (-1,3), B = (3,6), C = (3,3)

Distance formula:
`(x_1,y_1),(x_2,y_2)`

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance of AB: A = (-1,3), B = (3,6)

`AB=√((3-(-1))^2+(6-3)^2)`

`AB=√((4)^2+(3)^2)=5 units`

Distance of BC: B = (3,6) , C = (3,3)

`BC=√((3-3)^2+(3-6)^2)`

`BC=√((0)^2+(-3)^2)=3 units`

Distance of CA: C = (3,3) , A = (-1,3)

`CA=√(((-1)-3)^2+(3-3)^2)`

`CA=√((-4)^2+(0)^2)=4 units`

Perimeter of the triangle ABC = AB +BC + CA

= 5 units + 3 units + 4 units = 12 units

12 units is the perimeter of triangle ABC.