Question

1. if g is the mid - point of $overline{fh}$, $fg = 14x + 25$ and $gh = 73 - 2x$, find $overline{fh}$.

Explanation:

Step1: Set up the equation

Since G is the mid - point of $\overline{FH}$, then $FG = GH$. So we set up the equation $14x + 25=73 - 2x$.

Step2: Solve for x

Add $2x$ to both sides: $14x+2x + 25=73-2x + 2x$, which simplifies to $16x+25 = 73$. Then subtract 25 from both sides: $16x+25 - 25=73 - 25$, getting $16x=48$. Divide both sides by 16: $x=\frac{48}{16}=3$.

Step3: Find the length of $FG$ and $GH$

Substitute $x = 3$ into the expression for $FG$: $FG=14\times3 + 25=42 + 25 = 67$. Substitute $x = 3$ into the expression for $GH$: $GH=73-2\times3=73 - 6 = 67$.

Step4: Find the length of $\overline{FH}$

Since $FH=FG + GH$ and $FG = GH = 67$, then $FH=67+67 = 134$.

Answer:

134