https://file.aiquickdraw.com/mathbot/file/1726769754616zfdnn1of.jpg

This is a geometry problem involving similar triangles. From the image, we can observe that:

- \( \overline{PQ} \parallel \overline{HI} \), meaning the two triangles \( \triangle GPQ \) and \( \triangle GHI \) are similar by AA (Angle-Angle) similarity.
- In similar triangles, the corresponding sides are proportional.

Let's use the following information from the diagram:

- \( \overline{GP} = 10 \), \( \overline{GQ} = 15 \), \( \overline{HI} = 24 \)
- We need to find \( \overline{GH} \).

Using the property of similar triangles:

\[
\frac{GP}{GH} = \frac{GQ}{HI}
\]

Substituting the known values:

\[
\frac{10}{GH} = \frac{15}{24}
\]

Now, solving for \( GH \):

\[
GH = \frac{10 \times 24}{15}
\]

Let me calculate that.It seems I made an error. The initial calculation suggests that \( GH = 16 \), but that contradicts the diagram options. Let me recheck.

The correct relation involves using proportions with a larger triangle.

Let's solve this again properly!

Given: PQ is parallel to HI. Find the length of GH.

Learn how to find the length of GH using similar triangles and proportions in this geometry problem. With PQ parallel to HI, triangles GPQ and GHI are similar, allowing the use of the AA similarity theorem to find the unknown side.

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