Question

What is the perimeter of △LMN?

Answer 1

the correct answer to your question is the last option.  i know this because i just took the test and passed!

Answer 2

Find out the perimeter of △LMN .

To prove

Formula

`Distance\ formula = \sqrt{{(x_(2) - x_(1))^(2) +{(y_(2) - y_(1))^(2) }`

Two points be L(2, 4) and M (-2,1)

Put in the formula

`Distance\ formula = \sqrt{{(-2-2)^(2) +{(1-4)^(2) }`

Solving the above

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

`LM = √(16+9)`

`LM= √(25)`

`√(25) = 5 unit`

Two points be M (-2,1) and N (-1,4)

`Distance\ formula = \sqrt{{(-1+2)^(2) +{(4-1)^(2) }`

Solving the above

`Distance\ formula = \sqrt{{(1)^(2) +{(3)^(2) }`

`MN= √(1+9)`

`MN = √(10\units)`

Two points be N (-1,4) and L (2,4)

`Distance\ formula = \sqrt{{(2+1)^(2) +{(4-4)^(2) }`

Solving the above

`NL = \sqrt{{(3)^(2) +{(0)^(2) }`

`NL = √(9)`

`√(9) = 3`

NL = 3 units

Perimeter of a △LMN = LM + MN +NL

`Perimeter = 5 + √(10) + 3\\ Perimeter = 8 +√(10)\ units`

Option (d) is correct .