In the accompanying diagram, triangle ABCis similar to triangle DEF, AC = 6, AB = BC = 12, and DF = 8. Find the perimeter of triangle DEF.

Question

it an isoslese triangle 6 and 8 are both base
my work
6+2=8
12+2=14
2(14)+6=p
24+6=28
I don't understand how to find the perimeter of triangle DEF with out knowing the sides

Answer 1

Two ways you can do this. Since ABC is similar to DEF, and DF/AC = 4/3, the other two sides are also 4/3 as big, making them each 16. So, the perimeter of DEF is 8+16+16=40

Or, since the scale factor is 4/3, the perimeter of DEF is 4/3 that of ABC. ABC's perimeter is 6+12+12=30, so DEF has perimeter 4/3 as big, or 40.