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denis23 [38]
3 years ago
15

What is the perimeter of △LMN?

Mathematics
2 answers:
MAVERICK [17]3 years ago
5 0

we know that

The distance 's formula between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Step 1

<u>Find the distance MN</u>

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

Substitute in the distance's formula

d=\sqrt{(4-1)^{2}+(-1+2)^{2}}

d=\sqrt{(3)^{2}+(1)^{2}}

dMN=\sqrt{10}\ units

Step 2

<u>Find the distance NL</u>

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

Substitute in the distance's formula

d=\sqrt{(4-4)^{2}+(2+1)^{2}}

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

dNL=3\ units

Step 3

<u>Find the distance LM</u>

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

Substitute in the distance's formula

d=\sqrt{(1-4)^{2}+(-2-2)^{2}}

d=\sqrt{(-3)^{2}+(-4)^{2}}

dLM=5\ units

Step 4

<u>Find the perimeter of the triangle LMN</u>

we know that

The perimeter of a triangle is equal to the sum of the three length sides

In this problem

Perimeter=MN+NL+LM

substitute the values in the formula

Perimeter=(\sqrt{10}+3+5)\ units

Perimeter=(8+\sqrt{10})\ units

therefore

<u>the answer is the option D</u>

the perimeter of the triangle LMN is equal to (8+\sqrt{10})\ units

svetoff [14.1K]3 years ago
3 0
I  solved this via the Pythagorean theorem. Side LM is 5 and side NM is 3.16. Side NL is also 3. 3+5+3.16=11.16. The decimal form of 8+sqrt(10) is 11.16. D is the answe



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