Question

in the figure below, g is between e and h, and f is the midpoint of \\(\overline{eg}\\). if \\(fg = 8\\) and \\(eh = 21\\), find \\(gh\\). \\(gh = \square\\)

Explanation:

Step1: Find the length of EG

Since F is the midpoint of \( \overline{EG} \), we know that \( EF = FG \). Given \( FG = 8 \), then \( EF = 8 \). So the length of \( EG \) is \( EF + FG = 8 + 8 = 16 \).

Step2: Find the length of GH

We know that \( EH = EG + GH \). Given \( EH = 21 \) and we found \( EG = 16 \), we can solve for \( GH \) by rearranging the formula: \( GH = EH - EG \). Substituting the values, we get \( GH = 21 - 16 = 5 \).

Answer:

\( 5 \)