Perimeter is 8 + √(10) units.
<u>Step-by-step explanation:</u>
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.
