Question

question
point g is on line segment $overline{fh}$. given $fh = 4x$, $gh = x$, and $fg = 2x + 10$, determine the numerical length of $overline{fg}$.

Explanation:

Step1: Use segment - addition postulate

Since $FH = FG+GH$, we have $4x=(2x + 10)+x$.

Step2: Solve the equation for $x$

$4x=2x + 10+x$, $4x=3x + 10$, $4x-3x=10$, $x = 10$.

Step3: Find the length of $FG$

Substitute $x = 10$ into $FG=2x + 10$, $FG=2\times10+10=30$.

Answer:

30