Question

Ray LH bisects Segment GK at L. GL = 5x -5 and GK = 8x +6. find GK

Answer 1

The line LH bisects segment GK, this means that it divides segment GK exactly trough its midpoint.

Segments GL is equal to segment LK and both add up to GK:

GK= GL + LK

GL=LK= 5x-5

Using this equality you have to replace the segments names by the given expressions and clear the value of x.

`\begin{gathered} GK=GL+LK \\ 8x+6=(5x-5)+(5x-5) \\ 8x+6=5x-5+5x-5 \\ 8x+6=10x-10 \\ 8x-10x=-10-6 \\ -2x=-16 \\ x=8 \end{gathered}`

Now you can use the value of x to calculate the length of GK

GK=8x+6=8*8+6=70