An equilateral triangle is dilated by a scale factor of 3. If a side of the original triangle is 6, what is the measure of a side of the new triangle?

Answer: 18 units.

Step-by-step explanation:

When a segment 'm' is dilated by a scale factor 'k', then the measure of new dilated segment will be 'km' [i. e. New side length = scale factor is multiplied to the original side-length].

Given : An equilateral triangle is dilated by a scale factor of 3.

[Note an equilateral triangle has all its side-lengths are equal.]

Side-length of the original triangle = 6 units

Then, the measure of a side of the new triangle = Scale factor x Original side-length

= 3 x 6 = 18 units

Hence, the measure of a side of the new triangle = 18 units.

18

Step-by-step explanation:

Let the side of the triangle be a and that of the new one be a'.

a'/a = 3/1 Insert the value of a

a'/6 = 3 Multiply each side by 6

a' = 18

The measure of a side of the new triangle is 18.