The triangle in the image shows that the segment $GJ$ is labeled as $2s$ and the segment $JI$ is labeled as $s + 28$, while point $H$ is marked above $J$, making the triangle a right triangle at $J$ (since there is a right-angle symbol there). The problem asks for the length of $GI$.

Since $GHI$ forms a right triangle, we can apply the Pythagorean theorem:

$GI^2 = GJ^2 + JI^2$

Now, substituting the values for $GJ$ and $JI$:

$GI^2 = (2s)^2 + (s + 28)^2$

First, simplify the equation:

$GI^2 = 4s^2 + (s^2 + 56s + 784)$ $GI^2 = 5s^2 + 56s + 784$

To find $GI$, we would need the value of $s$ to substitute into this equation. If $s$ is provided or can be derived from other information, we can substitute it to compute $GI$.

Would you like to provide the value of $s$, or should we proceed with solving the equation as is? Feel free to ask for more details or clarification.

Here are some related questions:

1. How does the Pythagorean theorem apply in this context?
2. What role does the right-angle at $J$ play in solving the problem?
3. Could $s$ be derived from another part of the problem?
4. How would the solution change if $s$ had a specific value, like 5 or 10?
5. What is the next step if $s$ remains unknown?

Tip: When using the Pythagorean theorem, always double-check for any hidden information about the triangle's side lengths or angles.