Question

g is the midpoint of $overline{fh}$. if $fg = 2x$ and $fh = 5x - 6$, what is $fh? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $G$ is the mid - point of $\overline{FH}$, then $FG=\frac{1}{2}FH$. Given $FG = 2x$ and $FH=5x - 6$, we have the equation $2x=\frac{1}{2}(5x - 6)$.

Step2: Solve the equation for $x$

Multiply both sides of the equation $2x=\frac{1}{2}(5x - 6)$ by 2 to get $4x=5x - 6$. Then subtract $4x$ from both sides: $0 = 5x-4x - 6$, which simplifies to $x = 6$.

Step3: Find the value of $FH$

Substitute $x = 6$ into the expression for $FH$. Since $FH=5x - 6$, then $FH=5\times6-6=30 - 6=24$.

Answer:

24