Question

question point g is on line segment $overline{fh}$. given $gh = 8,fh = 3x + 3$, and $fg = 2x$, determine the numerical length of $overline{fg}$.

Explanation:

Step1: Use segment - addition postulate

Since point $G$ is on line segment $\overline{FH}$, we know that $FG + GH=FH$.
Substitute the given expressions: $2x + 8=3x + 3$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $8=x + 3$.
Then subtract 3 from both sides: $x=8 - 3=5$.

Step3: Find the length of $FG$

Since $FG = 2x$, substitute $x = 5$ into the expression for $FG$.
$FG=2\times5 = 10$.

Answer:

10