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.