To find the measure of side \( KI \) in triangle \( IJK \), you can use the property of similar triangles, which states that the corresponding sides of similar triangles are proportional.
Given the information:
- The length of side \( FG \) corresponds to side \( IJ \).
- The length of side \( GH \) corresponds to side \( JK \).
- The length of side \( FH \) corresponds to side \( IK \).
From your question, though, you’ve provided lengths for the sides:
- \( FG = 8 \)
- \( GH = 32 \)
- \( FH = 4.7 \)
We don't have the actual lengths of \( IJ \), \( JK \), or \( IK \), but we can set up a proportion using the given lengths.
Assuming \( FG \) is the side corresponding to \( IJ \), then the proportion between the two triangles can be set up as follows:
\[ \frac{FG}{IJ} = \frac{GH}{JK} = \frac{FH}{IK} \]
Using arbitrary variables since we don’t have specific lengths for the triangle \( IJK \):
- Let \( IJ = x \)
- Let \( JK = y \)
- Let \( IK = z \)
Establishing the ratios using the known sides:
From side \( FG \) to side \( IJ \): \[ \frac{8}{x} \]
From side \( GH \) to side \( JK \): \[ \frac{32}{y} \]
From side \( FH \) to side \( IK \): \[ \frac{4.7}{z} \]
For these triangles to be similar: \[ \frac{8}{x} = \frac{32}{y} = \frac{4.7}{z} \]
To find \( KI \) (which is \( z \)), we need additional information like the corresponding sides or a scale factor. Without that, we cannot determine the exact value of \( KI \).
If you have specific values for sides \( IJ \) or \( JK \) given, we can proceed with those values. Please provide those, or a specific scale factor between the triangles if available!