On a coordinate plane, triangle L M N is shown. Point L is at (2, 4), point M is at (negative 2, 1), and point N is at (negative 1, 4). What is the perimeter of △LMN?
8 units 9 units 6 + StartRoot 10 EndRoot units 8 + StartRoot 10 EndRoot units

Perimeter is  8 + √(10) units.

Step-by-step explanation:

First we have to find the distance between the all the 3 points and then using the distances, we can find the sum of it, so that we will get the perimeter of the triangle.

The points are L(2,4) , M(-2,1) and N(-1,4)

Distance between the points can be found as,

√((x₂-x₁)² + (y₂-y₁)²)

Plugin the values in the given point, we will get LM as,

LM = √((-2-2)² + (1-4)²)

    = √((-4)² + (-3)²)

   = √(16 + 9) = √(25) = 5 units.

MN = √((-1-(-2))² + (4-1)²)

     = √((-1+2))² + (4-1)²)

    = √((1))² + (3)²)

    = √(1 + 9) = √(10)

 NL = √((2-(-1))² + (4-4)²)

      = √((3)² + 0²) = √(9) = 3 units

Perimeter = LM + MN + NL = 5+ √(10) + 3 = 8 + √(10) units.

x is variable or an unknown value to find

example:

2x = 5 which means x = 3