The measure of side GH is 50.486 units.
Two triangles are similar if they share the same set of internal angles, that is, the following conditions are met:
[tex]\angle C \cong \angle F[/tex] (1)
[tex]\angle E \cong \angle H[/tex] (2)
[tex]\angle D \cong \angle G[/tex] (3)
Then, we can determine the length of the line segment [tex]GH[/tex] by the following relationship:
[tex]\frac{CD}{FG} = \frac{DE}{GH}[/tex] (4)
If we know that [tex]CD = 7[/tex], [tex]FG = 31[/tex] and [tex]DE = 11.4[/tex], then the value of the line segment [tex]GH[/tex] is:
[tex]GH = \frac{FG\cdot DE}{CD}[/tex]
[tex]GH = \frac{31\cdot 11.4}{7}[/tex]
[tex]GH = 50.486[/tex]
The measure of side GH is 50.486 units.
To learn more on similar triangles, we kindly invite to check this verified question: https://brainly.com/question/25882965
