Question

applying the side-splitter theorem
what is the length of \\(\overline{gd}\\)?
\\(gd = \square\\)
(there is a triangle - like figure with points e, f, d. segment ef has a mark, segment gh (connecting g on ed and h on fd) has a mark. length from e to g is 6, from f to h is 8, from h to d is 14.)

Explanation:

Step1: Identify Side-Splitter ratios

$\frac{EG}{GD} = \frac{FH}{HD}$
Given $EG=6$, $FH=8$, $HD=14$
Let $GD=x$, so $\frac{6}{x} = \frac{8}{14}$

Step2: Solve for x

Cross-multiply: $8x = 6×14$
$8x = 84$
$x = \frac{84}{8} = 10.5$

Answer:

10.5