If triangle abc is dilated by a scale factor of 2 with a center of dilation at vertex c, how does the perimeter of a'b'c' compare with the perimeter of abc?
a) the perimeter of a'b'c' is 2 times the perimeter of abc.
b) the perimeter of a'b'c' is 4 times the perimeter of abc.
c) the perimeter of a'b'c' is 6 times the perimeter of abc.
d) the perimeter of a'b'c' is 8 times the perimeter of abc.

In the given figure the sides of triangle measures as follows:

AB= 4 units,

BC= 6 units,

Since triangle ABC is right angled triangle, to find AC we will have to use Pythagorean theorem,

AB² + BC² = AC²

Plugging the values of AB and BC to find AC,

4² + 6² = AC²

16+36=AC²

AC = 7.48

Now if the triangle is dilated by a scale factor of 2, each side will be multiplied by 2 to get the new triangle A'B'C'

side A'B' = 2* AB = 2*4= 8 units

side B'C' = 2* BC = 2*6 =12 units

side A'C' = 2*AC = 2*7.48 = 14.96 units

Perimeter of triangle = sum of three sides

Perimeter of triangle A'B'C' = A'B' + B'C' + A'C'= 8+12 + 14.96 = 34.96 units.

Perimeter of triangle ABC = AB+BC + AC = 4+6+7.48 = 17.48 units.

Perimeter of triangle A'B'C' = 2* Perimeter of triangle ABC

The perimeter of new triangle A'B'C' is 34.96 units which is twice that of triangle ABC.

Answer : A) The perimeter of A'B'C' is 2 times the perimeter of ABC.