geometry question

Question

 

Let triangle ABC and triangle DEF be similar triangles such that the scale factor of triangle ABC and DEF is (2/3). The perimeter of triangle ABC is 20 inches. What is the perimeter of triangle DEF in inches?

 

A) 13

B) 25

C)30

D)40

E)45

 

 

PLEASE SHOW ALL WORK. THANKS AGAIN!!!!!!!!

Answer 1

Since triangle ABC is similar to triangle DEF, their perimeters are in proportion. So since the perimeter of triangle ABC is 20 inches and the scale factor from triangle ABC to DEF is 2/3, then the perimeter, P, of triangle DEF is such that 20/P = 2/3. Therefore P = 30, and the answer is C).