Question

use the figure below to answer questions #15 - 18. g is the midpoint of fh. 10x 7x + 15 f g h #15: x = ___ 1 point your answer #16: fg = _ 1 point your answer #17: gh = _ 1 point your answer #18: fh = ___ 1 point your answer

Explanation:

Step1: Set up equation using mid - point property

Since G is the midpoint of $\overline{FH}$, then $FG = GH$. So, $10x=7x + 15$.

Step2: Solve for x

Subtract $7x$ from both sides of the equation: $10x-7x=7x + 15-7x$. This gives $3x=15$. Then divide both sides by 3: $x=\frac{15}{3}=5$.

Step3: Find FG

Substitute $x = 5$ into the expression for $FG$. Since $FG = 10x$, then $FG=10\times5 = 50$.

Step4: Find GH

Since $GH=7x + 15$ and $x = 5$, then $GH=7\times5+15=35 + 15=50$.

Step5: Find FH

Since $FH=FG + GH$ and $FG = 50$ and $GH = 50$, then $FH=50+50 = 100$.

Answer:

#15: 5
#16: 50
#17: 50
#18: 100