https://file.aiquickdraw.com/mathbot/file/1728495546587s3nwag0d.jpg

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.

What is the length of GI in the right triangle, where GJ = 2s, JI = s + 28, and the triangle is a right triangle at J?

Learn how to find the length of GI in a right triangle, where GJ = 2s and JI = s + 28. This problem applies the Pythagorean theorem to solve for GI in terms of s. Perfect for students in Grades 8-10 looking to practice algebra and geometry.

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