Compute the ratio of the larger triangle's perimeter to the smaller triangle's perimeter. This ratio is the scale factor between the triangles.

Once you know how many times larger triangle $XYZ$ is compared with triangle $TUV$, multiply the given length $TU = 18$ by that scale factor to get $XY$.

In Desmos, type 18 * (333/37) and press Enter. The output is the value of $XY$, since $\dfrac{333}{37}$ is the scale factor from triangle $TUV$ to triangle $XYZ$.

For similar triangles, all linear measurements (like side lengths and perimeters) are multiplied by the same scale factor.

That means the ratio of the perimeters of triangles $XYZ$ and $TUV$ is the same as the ratio of any pair of corresponding sides, such as $XY$ and $TU$:

Substitute the given perimeter values into the ratio:

Now simplify $\frac{333}{37}$:

• $37 \times 9 = 333$, so

This means triangle $XYZ$ is 9 times larger (in linear dimensions) than triangle $TUV$, so

We are told $TU = 18$ and $\dfrac{XY}{TU} = 9$, so

Compute this product:

Therefore, the length of $\overline{XY}$ is 162.