Question

50 POINTS!!

In segment FH, the midpoint is G.

If segments FH = 14x - 4 and FG = 5x + 9, what is the measure of segment FH?


Draw this line segment and clearly label all points and given measures.

Answer 1

`FH=73`

Explanation:

We are given that a segment FH and G is the midpoint of FH.

FH=
`14x-4`

`FG=5x+9`

We have to find the measure of FH.

When G is the midpoint of segment FH

Then , FG=GH

`FH=FG+GH`

Segment addition property

`14x-4=FG+FG`

Substitution property

`14x-4=2FG`

`14x-4=2(5x+9)`

`14x-4=10x+18`

`14x-10x=18+4`

`4x=22`

`x=(22)/(4)=5.5`

Substitute the values then we get

`FG=5(5.5)+9=36.5`

`FG=GH=36.5`

`FH=14(5.5)-4=73`