Question

The vertices of triangle EFG are listed below.

What is the approximate perimeter of triangle EFG?

A. 21.21 units
B. 12.21 units
C. 36.05 units
D. 12.16 units

Answer 1

Option A.
`21.21\ units`

Explanation:

we know that

The perimeter of a triangle is equal to the sum of its three side lengths

so

`P=EF+FG+EG`

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

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

we have

`E(5,4),F(9,1),G(5,-5)`

step 1

Find the distance EF

`E(5,4),F(9,1)`

substitute in the formula

`EF=\sqrt{(1-4)^(2)+(9-5)^(2)}`

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

`EF=√(25)`

`EF=5\ units`

step 2

Find the distance FG

`F(9,1),G(5,-5)`

substitute in the formula

`FG=\sqrt{(-5-1)^(2)+(5-9)^(2)}`

`FG=\sqrt{(-6)^(2)+(-4)^(2)}`

`FG=√(52)`

`FG=7.21\ units`

step 3

Find the distance EG

`E(5,4),G(5,-5)`

substitute in the formula

`EG=\sqrt{(-5-4)^(2)+(5-5)^(2)}`

`EG=\sqrt{(-9)^(2)+(0)^(2)}`

`EG=√(81)`

`EG=9\ units`

step 4

Find the perimeter

`P=EF+FG+EG`

`P=5+7.21+9=21.21\ units`