Question

g is the midpoint of fh. if fg = 9x and gh = 5x + 7, what is gh? 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 $FG = GH$. So, $9x=5x + 7$.

Step2: Solve for x

Subtract $5x$ from both sides: $9x-5x=5x + 7-5x$. This gives $4x=7$. Then $x=\frac{7}{4}$.

Step3: Find the value of GH

Substitute $x = \frac{7}{4}$ into the expression for $GH$. $GH=5x + 7$. So, $GH=5\times\frac{7}{4}+7=\frac{35}{4}+7=\frac{35}{4}+\frac{28}{4}=\frac{35 + 28}{4}=\frac{63}{4}=15\frac{3}{4}$.

Answer:

$15\frac{3}{4}$