Question

can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the correct answer

Answer 1

Answer with step-by-step explanation:

The way the question is worded, this actually shouldn't be correct. The correct answer should be $3:4$.

Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.

Why?

By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.

Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are $\overline{RS}$ and $\overline{AB}$.

The ratio of $\overline{RS}:\overline{AB}$ is $18:24\implies \boxed{3:4}$.

The reason why it ideally should be $3:4$ and not $4:3$ is because the question states $RTSU\sim ABCD$, which mentions $RSTU$ first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.