How to get the answer for this?

NF = 16 units

Step-by-step explanation:

The in-center of a triangle is a point inside the triangle and equidistant from the three sides of the triangleIt is the center of the circle which touch the three sides of the triangle (each side of a triangle is tangent to the circle and the segments drawn from it to the points of tangent are radii of the circle)

∵ N is the in-center of ΔABC

∴ N is equidistant from the sides AB, BC and CA

- That means the perpendicular segments from N to AB, BC

   and AC are equal

∴ ND = NE = NF

∵ ND = 6x - 2

∵ NE = 3x + 7

- Equate them to find x

∴ 6x - 2 = 3x + 7

- Subtract 3x from both sides

∴ 3x - 2 = 7

- Add 2 to both sides

∴ 3x = 9

- Divide both sides by 3

∴ x = 3

- Substitute the value of x in ND to find its length

∵ ND = 6(3) - 2 = 18 - 2

∴ ND = 16 units

∵ ND = NE = NF

∴ NF = 16 units

Ican't do any of the other stuff, but i can get you started. the answer, i believe, is $2.50.

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