We are given two similar triangles, therefore, we have the following relationship:

Solving for VW:

Replacing in the equation:

Solving the operations:

Now we use the Pythagorean theorem to determine the length of WZ, that is:
![WZ=\sqrt[]{(VW)^2-(VZ)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/78douzt98mrtf7dmutqwbn93nnn13m3hf8.png)
Replacing:
![WZ=\sqrt[]{(21.6)^2-(44-27.5)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/lpaxmkmc5cimcay1i9v4r92kgm2h7owrhj.png)
Solving the operations:
![\begin{gathered} WZ=\sqrt[]{466.56-272.25} \\ WZ=\sqrt[]{194.31} \\ WZ=13.9 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/5a5mrfyatdbiwhdy508qdykjvux5zk05n5.png)
Now we find XY using the following relationship:

Solving for XY:

Replacing the values:

Solving the operations:

The perimeter of the figure is:

Replacing:

Solving the operations:
