3:2
1) Since those quadrilaterals are similar, they have proportional sides. Therefore we can use the Thales Theorem about similarity and write:
[tex]\begin{gathered} \frac{BC}{ST}=\frac{CD}{UT} \\ \frac{8}{12}=\frac{14}{UT} \\ 12\cdot14=8UT \\ UT=\frac{12\cdot14}{8} \\ UT=21 \end{gathered}[/tex]
2) Now we can find both perimeters since their opposite sides are congruent to each other.
2P (ABDC) = 8+8+14+14 = 16 +28 =44
2P( RSTU) = 2(12+21) = 2(33) = 66
3) Now we can write the ratio of Quadrilateral RSTU to ABCD
[tex]\frac{\text{RSTU}}{\text{ABCD}}=\frac{66}{44}=\frac{3}{2}[/tex]
Hence the ratio between the perimeter of RSTU to ABCD is 3:2
