The Question in the picture

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.