Question

figure below, g is between e and h, and f is the midpoint of \\( \overline { e g } \\). if \\( f g = 8 \\) and \\( f h = 12 \\), find e
h =

Explanation:

Step1: Find the length of \( FG \)

Since \( F \) is the mid - point of \( \overline{EG} \), we know that \( EF=FG \). Given \( FG = 8 \), so \( EF=8 \).

Step2: Find the length of \( GH \)

We know that \( FH=FG + GH \). Given \( FH = 12 \) and \( FG = 8 \), then \( GH=FH - FG \). Substitute the values: \( GH=12 - 8=4 \).

Step3: Calculate the length of \( EH \)

\( EH=EF + FG+GH \). Substitute \( EF = 8 \), \( FG = 8 \) and \( GH = 4 \) into the formula. \( EH=8 + 8+4 \).

Answer:

\( 20 \)