Question

What is the perimeter of △LMN?

8 units
9 units
6 + StartRoot 10 EndRoot units
8 + StartRoot 10 EndRoot units

Answer 1

its D on edg

Explanation:

Answer 2

The perimeter of △LMN is 8 +
`√(10)`

Explanation:

Step 1: Finding the length of LM

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= 2

`x_2`= -2

`y_1`= 4

`y_2`=1

LM =
`√((-2-2)^2 +(1-4)^2)`

LM =
`√((-4)^2 +(-3)^2)`

LM =
`√(16 +9))`

LM =
`√(25)`

LM = 5

Step 2: Finding the length of MN

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= -2

`x_2`= -1

`y_1`= 1

`y_2`= 4

LM =
`√((-1-(-2))^2 +(4 - 1)^2)`

LM =
`√((11+2)^2 +(3)^2)`

LM =
`√(1 +9))`

LM =
`√(10)`

Step 3 : Finding the length of NL

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_1)^2)`

here

`x_1`= -1

`x_2`= 2

`y_1`= 4

`y_2`= 4

NL =
`√((2-(-1))^2 +(4 - 4)^2)`

NL =
`√((3)^2 +0)`

NL =
`√(9 +0)`

B =
`√(9 )`

NL = 3

Step 4: Finding the perimeter of the triangle

Perimeter = length of LM + length of MN + length of NL

Perimeter = 5 +
`√(10)` + 3

Perimeter = 8 +
`√(10)`