Question

what is the perimeter of △lmn? 8 + √10 units 9 units 6 + √10 units 8 units

Explanation:

Step1: Identify coordinates of L, M, N

L(2,4), M(-2,1), N(-1,4)

Step2: Calculate ML distance

$ML = \sqrt{(-2-2)^2 + (1-4)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16+9} = 5$

Step3: Calculate LN distance

$LN = \sqrt{(-1-2)^2 + (4-4)^2} = \sqrt{(-3)^2 + 0^2} = 3$

Step4: Calculate MN distance

$MN = \sqrt{(-1-(-2))^2 + (4-1)^2} = \sqrt{(1)^2 + (3)^2} = \sqrt{1+9} = \sqrt{10}$

Step5: Sum to get perimeter

$Perimeter = ML + LN + MN = 5 + 3 + \sqrt{10} = 8 + \sqrt{10}$

Answer:

8 + √10 units