picture below
look at the picture.
1.
ef : ab = 2 : 3
gf : cb = 2 : 3
gh : cd = 2 : 3
he : da = 2 : 3
2.
∠a ≅ ∠e
∠b ≅ ∠f
∠c ≅ ∠g
∠d ≅ ∠h
3.
use pythagorean theorem:
the length of the abcd trapezoid sides:
|ab| = 3 cm
|bc| = 10 cm
|cd| = 3(3) cm = 9 cm
|da| = 8 cm
the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm
the ratio of perimeters of the tarapezoids is equal 2 : 3.
substitute:
cross multiply
divide both sides by 3