Question

A(-2,3)

B(3,0)
C (-4,-3)
What is the perimeter of the triangle? Round to the nearest tenth.

Answer 1

The perimeter of triangle is 19.8 units

Explanation:

we know that

The perimeter of triangle ABC is

`P=AB+BC+AC`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance AB

we have

`A(-2,3),B(3,0)`

substitute in the formula

`d=\sqrt{(0-3)^(2)+(3+2)^(2)}`

`d=\sqrt{(-3)^(2)+(5)^(2)}`

`d_A_B=√(34)\ units`

step 2

Find the distance BC

we have

`B(3,0),C (-4,-3)`

substitute in the formula

`d=\sqrt{(-3-0)^(2)+(-4-3)^(2)}`

`d=\sqrt{(-3)^(2)+(-7)^(2)}`

`d_B_C=√(58)\ units`

step 3

Find the distance AC

we have

`A(-2,3),C (-4,-3)`

substitute in the formula

`d=\sqrt{(-3-3)^(2)+(-4+2)^(2)}`

`d=\sqrt{(-6)^(2)+(-2)^(2)}`

`d_A_C=√(40)\ units`

step 4

Find the perimeter

`P=AB+BC+AC`

substitute the values

`P=√(34)+√(58)+√(40)`

`P=19.8\ units`